AI & ChatGPT searches , social queries for NU FUNCTION
Search references for NU FUNCTION. Phrases containing NU FUNCTION
See searches and references containing NU FUNCTION!
Search references for NU FUNCTION. Phrases containing NU FUNCTION
See searches and references containing NU FUNCTION!NU FUNCTION
Mathematical function
In mathematics, the nu function is a generalization of the reciprocal gamma function of the Laplace transform. Formally, it can be defined as ν ( x ) ≡
Nu_function
Family of solutions to related differential equations
Bessel functions in the form ∑ ν = − ∞ ∞ J N ν + p ( x ) {\textstyle \sum _{\nu =-\infty }^{\infty }J_{N\nu +p}(x)} where ν , p ∈ Z , N ∈ Z + \nu ,p\in
Bessel_function
Asymmetric sigmoid function
the generalized logistic function when X ( t ) = ( ν ν + 1 ) ν K {\displaystyle X(t)=\left({\frac {\nu }{\nu +1}}\right)^{\nu }K} and one in the graph
Gompertz_function
Probability distribution
\nu }}\,\Gamma {\left({\frac {\nu }{2}}\right)}}}&={\frac {(\nu -1)!!}{k{\sqrt {\nu }}(\nu -2)!!}}\\\end{aligned}}} The probability density function is
Student's_t-distribution
Ratio of the perimeter of Bernoulli's lemniscate to its diameter
The ν {\displaystyle \nu } function is closely related to the ξ {\displaystyle \xi } function which is the multiplicative function defined by ξ ( p n )
Lemniscate_constant
Function in statistics
In statistics, the generalized Marcum Q-function of order ν {\displaystyle \nu } is defined as Q ν ( a , b ) = 1 a ν − 1 ∫ b ∞ x ν exp ( − x 2 + a 2
Marcum_Q-function
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
delta (named after Leopold Kronecker) is a function of two variables, usually non-negative integers. The function is 1 if the variables are equal, and 0 otherwise:
Kronecker_delta
Thirteenth letter in the Greek alphabet
Nu (/ˈnjuː/ ; uppercase Ν, lowercase ν; Greek: vυ ny, [ni]) is the thirteenth letter of the Greek alphabet, representing the voiced alveolar nasal [n]
Nu_(Greek)
Mathematical function
(C+Qe^{-B(t-M)})^{1/\nu }}} this representation simplifies the setting of both a starting time and the value of Y {\displaystyle Y} at that time. The logistic function, with
Generalised_logistic_function
Distance function defined between probability distributions
{\displaystyle \nu } are probability distributions containing a total mass of 1. Assume also that there is given some cost function c ( x , y ) ≥ 0 {\displaystyle
Wasserstein_metric
{(q^{\nu +1};q)_{\infty }}{(q;q)_{\infty }}}x^{\nu }{}_{1}\phi _{1}(0;q^{\nu +1};q,qx^{2}).} ϕ {\displaystyle \phi } is the basic hypergeometric function.
Hahn–Exton_q-Bessel_function
\nu )\mathbf {J} _{\nu }(z)&=\cos(\pi \nu )\mathbf {E} _{\nu }(z)-\mathbf {E} _{-\nu }(z),\\-\sin(\pi \nu )\mathbf {E} _{\nu }(z)&=\cos(\pi \nu )\mathbf
Anger_function
Mathematical Function
{\displaystyle \chi _{\nu }(z)={\frac {1}{2}}\left[\operatorname {Li} _{\nu }(z)-\operatorname {Li} _{\nu }(-z)\right].} The Legendre chi function appears as the
Legendre_chi_function
Mathematical functions
doi:10.1007/BF02547966. See eq. (9) For more on the ν {\displaystyle \nu } function, see Lemniscate constant. Hurwitz, Adolf (1963). Mathematische Werke:
Lemniscate_elliptic_functions
Tool in multivariate statistical analysis
is the gamma function, K ν {\displaystyle K_{\nu }} is the modified Bessel function of the second kind, and ρ and ν {\displaystyle \nu } are positive
Matérn_covariance_function
Expressing a measure as an integral of another
{\displaystyle d\nu /d\mu } and is called the Radon–Nikodym derivative. The choice of notation and the name of the function reflects the fact that the function is analogous
Radon–Nikodym_theorem
\displaystyle k_{\nu }(x)={\frac {2}{\pi }}\int _{0}^{\pi /2}\cos(x\tan \theta -\nu \theta )\,d\theta .} Bateman discovered this function, when Theodore
Bateman_function
{d^{2}y}{dz^{2}}}+z{\frac {dy}{dz}}+(z^{2}-\nu ^{2})y=z^{\mu +1}.} Solutions are given by the Lommel functions sμ,ν(z) and Sμ,ν(z), introduced by Eugen von
Lommel_function
Relation between peak wavelengths of black body radiation and temperature
law as a function of frequency ν {\displaystyle \nu } : u ν ( ν , T ) = 2 h ν 3 c 2 1 e h ν / k T − 1 . {\displaystyle u_{\nu }(\nu ,T)={2h\nu ^{3} \over
Wien's_displacement_law
Characteristic of an optical system
ν ⋅ x ) {\displaystyle 1+\cos(2\pi \nu \cdot x)} , as a function of the spatial frequency, ν {\displaystyle \nu } , while its complex argument indicates
Optical_transfer_function
Buchholz's psi-functions are a hierarchy of single-argument ordinal functions ψ ν ( α ) {\displaystyle \psi _{\nu }(\alpha )} introduced by German mathematician
Buchholz_psi_functions
Spectral density of light emitted by a black body
) {\displaystyle B_{\nu }(\nu ,T)} by the substitution λ = c / ν {\displaystyle \lambda =c/\nu } . These are different functions because the spectral
Planck's_law
Form of continuity for functions
with respect to ν , {\displaystyle \nu ,} which means that there exists a ν {\displaystyle \nu } -measurable function f {\displaystyle f} taking values
Absolute_continuity
Mathematical function
^{2}(x)+\pi ^{2}}}\,dx} Bessel–Clifford function Inverse-gamma distribution Nu function Weisstein, Eric W. "Gamma function". mathworld.wolfram.com. Retrieved
Reciprocal_gamma_function
Probability distribution
function of the inverse chi-squared distribution is given by f ( x ; ν ) = 2 − ν / 2 Γ ( ν / 2 ) x − ν / 2 − 1 e − 1 / ( 2 x ) {\displaystyle f(x;\nu
Inverse-chi-squared distribution
Inverse-chi-squared_distribution
Concept in statistics
}{\mathcal {W}}(x\mid \mu ,\nu )e^{itx},dx.} For every fixed ( μ , ν ) {\displaystyle (\mu ,\nu )} , this is the characteristic function of the measured random
Kernel_density_estimation
) {\displaystyle -ix^{-1/2}J_{\nu +1}^{(2)}(ix^{1/2};q)/J_{\nu }^{(2)}(ix^{1/2};q)} is a completely monotonic function (Ismail (1982)). The first and
Jackson_q-Bessel_function
Multivalued function in mathematics
_{-\pi }^{\pi }{\frac {\left(1-\nu \cot \nu \right)^{2}+\nu ^{2}}{z+\nu \csc \left(\nu \right)e^{-\nu \cot \nu }}}\,d\nu \\[5pt]&={\frac {z}{\pi }}\int
Lambert_W_function
Concept in mathematics
}(z)=e^{-{\frac {1}{4}}z^{2}}z^{\nu }\left(1-{\frac {\nu (\nu -1)}{2}}{\frac {1}{z^{2}}}+{\frac {\nu (\nu -1)(\nu -2)(\nu -3)}{8}}{\frac {1}{z^{4}}}-\dots
Parabolic_cylinder_function
Probability distribution
{\Psi } ^{-1},\nu )} . Important identities have been derived for the inverse-Wishart distribution. The probability density function of the inverse Wishart
Inverse-Wishart_distribution
{\sqrt {M^{2}-1}}\end{aligned}}} where ν {\displaystyle \nu \,} is the Prandtl–Meyer function, M {\displaystyle M} is the Mach number of the flow and γ
Prandtl–Meyer_function
Type of polynomial used in Numerical Analysis
n {\displaystyle b_{\nu ,n}(1)=\delta _{\nu ,n}} where δ i , j {\displaystyle \delta _{i,j}} is the Kronecker delta function: δ i j = { 0 if i ≠ j
Bernstein_polynomial
Probability distribution
_{0}^{2}}{2\sigma ^{2}}}\right]}{(\sigma ^{2})^{1+{\frac {\nu _{0}}{2}}}}}} The likelihood function from above, written in terms of the variance, is: p ( X
Normal_distribution
Optical device with parallel mirrors
{\displaystyle \tau _{c}(\nu )} and linewidth Δ ν c ( ν ) {\displaystyle \Delta \nu _{c}(\nu )} now become local functions of frequency. Whereas the photon
Fabry–Pérot_interferometer
Type of mathematical functions
^{n};\left|\zeta _{\nu }-z_{\nu }\right|\leq r_{\nu }{\text{ for all }}\nu =1,\dots ,n\right\}} and let { z ν } ν = 1 n {\displaystyle \{z_{\nu }\}_{\nu =1}^{n}}
Function of several complex variables
Function_of_several_complex_variables
Brazilian financial technology company
Nubank, doing business outside of Brazil as Nu, is a Brazilian neobank headquartered in São Paulo, Brazil. Although it is not formally part of Brazil’s
Nubank
Approximation of a black body's spectral radiance
) {\displaystyle I(\nu ,T)=\pi B_{\nu }(T)} for emitted power integrated over all solid angles. In this form, the Planck function and associated Rayleigh–Jeans
Rayleigh–Jeans_law
Probability distribution
probability density function is f ( x ∣ ν , σ ) = x σ 2 exp ( − ( x 2 + ν 2 ) 2 σ 2 ) I 0 ( x ν σ 2 ) H ( x ) , {\displaystyle f(x\mid \nu ,\sigma )={\frac
Rice_distribution
Study of optimal transportation and allocation of resources
be a Borel-measurable function. Given probability measures μ {\displaystyle \mu } on X {\displaystyle X} and ν {\displaystyle \nu } on Y {\displaystyle
Transportation theory (mathematics)
Transportation_theory_(mathematics)
Probability distribution
g(\alpha )={\frac {\nu _{U}(\alpha )-\nu (\alpha )}{\nu _{U}(\alpha )-\nu _{L\infty }(\alpha )}}} For the simplest interpolating function considered, a first-order
Gamma_distribution
2 ν − ν + ε ) , ν = 1 , … , k . {\displaystyle (2^{\nu },2^{\nu }-\nu +\varepsilon ),\quad \nu =1,\ldots ,k.} Hua Loo-keng (1938). "On Waring's problem"
Hua's_lemma
Probability distribution
=Q\left({\frac {\nu }{2}},{\frac {\tau ^{2}\nu }{2x}}\right)} where Γ ( a , x ) {\displaystyle \Gamma (a,x)} is the incomplete gamma function, Γ ( x ) {\displaystyle
Scaled inverse chi-squared distribution
Scaled_inverse_chi-squared_distribution
=2\pi c{\tilde {\nu }}} where c is the speed of light in vacuum. In terms of the vibrational wavenumbers we can write the partition function as Q vib ( T
Vibrational partition function
Vibrational_partition_function
Mathematical rule
\mu ,\nu } , of which λ {\displaystyle \lambda } and μ {\displaystyle \mu } describe the Schur functions being multiplied, and ν {\displaystyle \nu } gives
Littlewood–Richardson_rule
Multivariate continuous probability distribution
};{\mathbf {\Psi } },\nu ,\delta )={\frac {\Gamma _{p}\left({\frac {\nu +\delta +p-1}{2}}\right)}{\Gamma _{p}\left({\frac {\nu }{2}}\right)\Gamma _{p}\left({\frac
Matrix_F-distribution
Probability distribution
mass function P ( X = x ) = f ( x ; λ , ν ) = λ x ( x ! ) ν 1 Z ( λ , ν ) . {\displaystyle P(X=x)=f(x;\lambda ,\nu )={\frac {\lambda ^{x}}{(x!)^{\nu }}}{\frac
Conway–Maxwell–Poisson distribution
Conway–Maxwell–Poisson_distribution
Extension of the factorial function
Jerome (2010). "Chapter 43 - The Gamma Function Γ ( ν ) {\displaystyle \Gamma (\nu )} ". An Atlas of Functions (2 ed.). New York, NY: Springer Science
Gamma_function
Theorem in optimal transport
measure is the gradient of a convex function. More precisely, if μ {\displaystyle \mu } and ν {\displaystyle \nu } are probability measures on R n {\displaystyle
Brenier's_theorem
Sequence of differential equation solutions
{\displaystyle J_{\alpha }} is a Bessel function of the first kind. See also:. Let ν = 4 n + 2 α + 2 {\displaystyle \nu =4n+2\alpha +2} . Let Ai {\displaystyle
Laguerre_polynomials
the Kelvin functions berν(x) and beiν(x) are the real and imaginary parts, respectively, of J ν ( x e 3 π i 4 ) , {\displaystyle J_{\nu }\left(xe^{\frac
Kelvin_functions
Family of continuous probability distributions
on ( 0 , ∞ ) {\displaystyle (0,\infty )} . Its probability density function is given by f ( x ; μ , λ ) = λ 2 π x 3 exp ( − λ ( x − μ ) 2 2 μ 2 x
Inverse_Gaussian_distribution
Partial order between random variables
distribution functions of two distinct investments ρ {\displaystyle \rho } and ν {\displaystyle \nu } . ρ {\displaystyle \rho } dominates ν {\displaystyle \nu }
Stochastic_dominance
Electronic musician
The Collapse of the Wave Function EPs take a more experimental direction. Albums Sound of the Street (1996) Ffressshh! (1997) Nu Romantix (1998) We are
DMX_Krew
Generalization of the indicator function for classical sets in fuzzy logic
as a function, ν {\displaystyle \nu } from S, the set of subsets of some set, into [ 0 , 1 ] {\displaystyle [0,1]} , such that ν {\displaystyle \nu } is
Membership function (mathematics)
Membership_function_(mathematics)
Mathematical theorem
{(-1)^{k}}{\Gamma (k+\nu +1)k!}}{\bigg (}{\frac {z}{2}}{\bigg )}^{2k+\nu }} By Ramanujan's master theorem, together with some identities for the gamma function and rearranging
Ramanujan's_master_theorem
Quantum field theory
{\displaystyle \ F_{\mu \nu }^{a}=\partial _{\mu }A_{\nu }^{a}-\partial _{\nu }A_{\mu }^{a}+g\ f^{abc}\ A_{\mu }^{b}\ A_{\nu }^{c}\ } can be derived by
Yang–Mills_theory
Type of weapon invented in China
pinyin: Lián Nǔ), also known as the repeater crossbow, and the Zhuge crossbow (Chinese: 諸葛弩; pinyin: Zhūgě nǔ, also romanized Chu-ko-nu) due to its association
Repeating_crossbow
Partial differential equation
t}}-\nu {\frac {\partial ^{2}\varphi }{\partial x^{2}}}=\varphi {\frac {df(t)}{dt}},} where d f / d t {\displaystyle df/dt} is an arbitrary function of
Burgers'_equation
Function in quantum field theory showing probability amplitudes of moving particles
}p^{\mu }\gamma _{\nu }p^{\nu }+\gamma _{\nu }p^{\nu }\gamma _{\mu }p^{\mu })\\[6pt]&={\tfrac {1}{2}}(\gamma _{\mu }\gamma _{\nu }+\gamma _{\nu }\gamma _{\mu
Propagator
Special function occurring in problems possessing elliptic symmetry
In mathematics, Mathieu functions, sometimes called angular Mathieu functions, are solutions of Mathieu's differential equation d 2 y d x 2 + ( a − 2
Mathieu_function
Theory of behavioral economics
{\displaystyle \nu (y)+\nu (-y)>\nu (x)+\nu (-x)} and ν ( − y ) + ν ( − x ) > ν ( x ) + ν ( − x ) {\displaystyle \nu (-y)+\nu (-x)>\nu (x)+\nu (-x)} . The
Prospect_theory
Equation in Fourier analysis
}s(\lambda )={\frac {1}{m(V/\Lambda )}}\sum _{\nu \in \Lambda '}S(\nu )} This is applied in the theory of theta functions and is a possible method in geometry of
Poisson_summation_formula
Method of solution to differential equations
Heaviside step function, J ν ( z ) {\textstyle J_{\nu }(z)} is a Bessel function, I ν ( z ) {\textstyle I_{\nu }(z)} is a modified Bessel function of the first
Green's_function
Statement in complex analysis; formerly the Bieberbach conjecture
| 2 {\displaystyle \sum _{n=1}^{\infty }(\nu +n)\sigma _{n}|a_{n}|^{2}} is achieved by the Koebe function z / ( 1 − z ) 2 {\displaystyle z/(1-z)^{2}}
De_Branges's_theorem
f_{\text{R}}(q;k,\nu )={\frac {{\sqrt {2\pi \,}}\,k\,(k-1)\,\nu ^{\nu /2}}{\Gamma (\nu /2)\,2^{\left(\nu /2-1\right)}}}\int _{0}^{\infty }s^{\nu }\,\varphi ({\sqrt
Studentized range distribution
Studentized_range_distribution
Release of a photon triggered by another
ν = ν 0 {\displaystyle \nu =\nu _{0}} . A line shape function can be normalized so that its value at ν 0 {\displaystyle \nu _{0}} is unity; in the case
Stimulated_emission
Measure of local oscillation behavior
\nu )={\frac {1}{2}}\sum _{x}\left|\mu (x)-\nu (x)\right|} The total variation of a C 1 ( Ω ¯ ) {\displaystyle C^{1}({\overline {\Omega }})} function f
Total_variation
Imaging Instrument
}c_{\nu }(t)\psi _{\nu }^{\text{T}}(t)} with the initial condition c ν ( 0 ) = 0 {\displaystyle c_{\nu }(0)=0} . When the new wave function is inserted into
Scanning_tunneling_microscope
Law of wavelength-specific emission and absorption
{\displaystyle S_{\nu }=k_{B}\left[\left(1+{\frac {E}{h\nu }}\right)\ln \left(1+{\frac {E}{h\nu }}\right)-{\frac {E}{h\nu }}\ln {\frac {E}{h\nu }}\right]} for
Kirchhoff's law of thermal radiation
Kirchhoff's_law_of_thermal_radiation
Principle in mathematical optimization
_{i=1}^{m}\lambda _{i}f_{i}(x)+\sum _{i=1}^{p}\nu _{i}h_{i}(x)\right\}.} The dual function g {\displaystyle g} is concave, even when the initial
Duality_(optimization)
Polynomial sequence
{\begin{aligned}C_{\nu }(x)&=-C_{\nu }(1-x)\\S_{\nu }(x)&=S_{\nu }(1-x).\end{aligned}}} They are related to the Legendre chi function χ ν {\displaystyle \chi _{\nu }}
Bernoulli_polynomials
Local theory of several complex variables
T_{n}(k)=\left\{\sum _{\nu _{1},\dots ,\nu _{n}\geq 0}a_{\nu _{1},\dots ,\nu _{n}}X_{1}^{\nu _{1}}\cdots X_{n}^{\nu _{n}},|a_{\nu _{1},\dots ,\nu _{n}}|\to 0{\text{
Weierstrass preparation theorem
Weierstrass_preparation_theorem
Mathematical function with no sudden changes
In mathematics, a continuous function is a function such that a small variation of its argument induces at most a small variation of its value. This implies
Continuous_function
Two-dimensional laminar boundary layer that forms on a semi-infinite plate
{\partial u}{\partial y}}=-{\dfrac {1}{\rho }}{\dfrac {\partial p}{\partial x}}+{\nu }{\dfrac {\partial ^{2}u}{\partial y^{2}}}} y {\displaystyle y} -Momentum:
Blasius_boundary_layer
Mathematical operation
{\displaystyle \nu } of a function f(r) is given by F ν ( k ) = ∫ 0 ∞ f ( r ) J ν ( k r ) r d r , {\displaystyle F_{\nu }(k)=\int _{0}^{\infty }f(r)J_{\nu }(kr)\
Hankel_transform
Probability distribution
{\frac {\nu }{2}}\right)\right],} I y ( a , b ) {\displaystyle I_{y}\,\!(a,b)} is the regularized incomplete beta function, y = x 2 x 2 + ν
Noncentral_t-distribution
Concept in mathematics
{\displaystyle \displaystyle J_{m+\nu }(z)=J_{\nu }(z)R_{m,\nu }(z)-J_{\nu -1}(z)R_{m-1,\nu +1}(z)} where Jν(z) is a Bessel function of the first kind. They are
Lommel_polynomial
Quantum field theory enjoying conformal symmetry
{\displaystyle T_{\mu \nu }\xi ^{\nu }} where ξ ν {\displaystyle \xi ^{\nu }} is a Killing vector and T μ ν {\displaystyle T_{\mu \nu }} is a conserved operator
Conformal_field_theory
Inverse of a finite difference
{\displaystyle \sum _{\nu =x}^{y}(\lambda f(\nu )+\mu g(\nu ))=\lambda \sum _{\nu =x}^{y}f(\nu )+\mu \sum _{\nu =x}^{y}g(\nu )} . Empty Sum Condition:
Indefinite_sum
G_{\nu }(\omega )=e^{j(\nu -2)[{\frac {\omega -\pi }{2}}]}.{\frac {ce_{\nu }({\frac {\omega -\pi }{2}},q)}{ce_{\nu }(0,q)}}.} The transfer function of
Mathieu_wavelet
Generalization of the Jack polynomial
In mathematics, the Jack function is a generalization of the Jack polynomial, introduced by Henry Jack. The Jack polynomial is a homogeneous, symmetric
Jack_function
surely cdf cumulative distribution function cmf cumulative mass function df degrees of freedom (also ν {\displaystyle \nu } ) i.i.d. independent and identically
Notation in probability and statistics
Notation_in_probability_and_statistics
Type of wavelet
{\displaystyle \nu } . The low-pass filter transfer function is given by H ν ( ω ) = − e − j ν ω − π 2 P ν ( cos ( ω 2 ) ) {\displaystyle H_{\nu }(\omega )=-e^{-j\nu
Legendre_wavelet
Generalization of the hypergeometric function
{i}{\pi }}ye^{-\nu \pi i}\left[e^{\pi y}A(\nu +iy,\nu -iy\,|\,ze^{i\pi })-e^{-\pi y}A(\nu -iy,\nu +iy\,|\,ze^{i\pi })\right],} where the function A(·) is defined
Meijer_G-function
Classical physics prediction that black body radiation grows unbounded with frequency
frequency ν {\displaystyle \nu } , the expression is instead B ν ( T ) = 2 ν 2 k B T c 2 . {\displaystyle B_{\nu }(T)={\frac {2\nu ^{2}k_{\mathrm {B} }T}{c^{2}}}
Ultraviolet_catastrophe
Concept in statistics
the multivariate gamma function. If X ∼ T n × p ( ν , M , Σ , Ω ) {\displaystyle \mathbf {X} \sim {\mathcal {T}}_{n\times p}(\nu ,\mathbf {M} ,\mathbf
Matrix_t-distribution
Subadditive or superadditive integral
{\displaystyle (C)\int \,fd\nu +(C)\int g\,d\nu \leq (C)\int (f+g)\,d\nu .} Let G {\displaystyle G} denote a cumulative distribution function such that G − 1 {\displaystyle
Choquet_integral
Special functions of several complex variables
mathematics, theta functions are special functions of several complex variables. Fundamentally, they are a family of continuous functions which encode the
Theta_function
Class of probability distributions
\operatorname {Var} (X)=V(\mu )=\nu _{0}+\nu _{1}\mu +\nu _{2}\mu ^{2},} then the new NEF-QVF has variance function Var ( Y ) = V ∗ ( μ ∗ ) = ν 0 ∗
Natural_exponential_family
B {\displaystyle \theta _{\text{vib}}={\frac {h{\tilde {\nu }}c}{k_{\text{B}}}}={\frac {h\nu }{k_{\text{B}}}}} where k B {\displaystyle k_{\text{B}}}
Vibrational_temperature
Quantum field theory of electromagnetism
_{\nu }\left({\frac {\partial {\mathcal {L}}}{\partial (\partial _{\nu }A_{\mu })}}\right)=\partial _{\nu }\left(\partial ^{\mu }A^{\nu }-\partial ^{\nu
Quantum_electrodynamics
Measure of divisibility by a prime number
{\displaystyle m} . In particular, ν p {\displaystyle \nu _{p}} is a function ν p : Z → N 0 ∪ { ∞ } {\displaystyle \nu _{p}\colon \mathbb {Z} \to \mathbb {N} _{0}\cup
P-adic_valuation
Theorem in mathematical measure theory
{\displaystyle \nu _{0}} and ν 1 {\displaystyle \nu _{1}} such that: ν = ν 0 + ν 1 {\displaystyle \nu =\nu _{0}+\nu _{1}\,} ν 0 ≪ μ {\displaystyle \nu _{0}\ll
Lebesgue's decomposition theorem
Lebesgue's_decomposition_theorem
Statistical test of whether two populations have equal means
{s_{2}^{4}}{N_{2}^{2}\nu _{2}}}}}={\frac {s_{\Delta {\bar {X}}}^{4}}{{\frac {s_{{\bar {X}}_{1}}^{4}}{\nu _{1}}}+{\frac {s_{{\bar {X}}_{2}}^{4}}{\nu _{2}}}}},} where
Welch's_t-test
Seventh letter in the Greek alphabet
Greek dialects to represent the voiceless glottal fricative, [h]. In this function, it was borrowed in the 8th century BC by the Etruscan and other Old Italic
Eta
Class of inequalities
|}f(x){\big |}^{2}\log {\big |}f(x){\big |}\,d\nu (x)\leq \int _{\mathbb {R} ^{n}}{\big |}\nabla f(x){\big |}^{2}\,d\nu (x)+\|f\|_{2}^{2}\log \|f\|_{2},} where
Logarithmic Sobolev inequalities
Logarithmic_Sobolev_inequalities
and the ν {\displaystyle \nu } degree are real, and assume x ∈ ( − 1 , + 1 ) {\displaystyle x\in (-1,+1)} . Ferrers function of the first kind P v μ (
Ferrers_function
Continuous probability distribution
{|\alpha |\beta ^{\nu }}{\Gamma \left(\nu \right)}}x^{\alpha \nu -1}\exp _{\kappa }(-\beta x^{\alpha })} . The cumulative distribution function of κ-Gamma distribution
Kaniadakis_Gamma_distribution
this type incomplete-version of Bessel function or this type generalized-version of incomplete gamma function: K v ( x , y ) = ∫ 1 ∞ e − x t − y t t v
Incomplete Bessel K function/generalized incomplete gamma function
Incomplete_Bessel_K_function/generalized_incomplete_gamma_function
Measure of material deformation perpendicular to loading
In materials science and solid mechanics, Poisson's ratio (symbol: ν (nu)) is a measure of the Poisson effect, the deformation (expansion or contraction)
Poisson's_ratio
NU FUNCTION
NU FUNCTION
NU FUNCTION
NU FUNCTION
NU FUNCTION
NU FUNCTION
NU FUNCTION
NU FUNCTION
NU FUNCTION