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Inverse of a finite difference
calculus of finite differences, the indefinite sum (or antidifference operator), denoted by ∑ x {\textstyle \sum _{x}} or Δ − 1 {\displaystyle \Delta
Indefinite_sum
This is a list of indefinite sums (also known as antidifferences) of various functions. An indefinite sum ∑ x f ( x ) {\textstyle \sum _{x}f(x)} is the
List_of_indefinite_sums
Mathematical concept
{\displaystyle \prod _{x}f(Tx)=Cf(Tx)^{x-1}} Indefinite product can be expressed in terms of indefinite sum: ∏ x f ( x ) = exp ( ∑ x ln f ( x ) ) {\displaystyle
Indefinite_product
Topics referred to by the same term
contracting tensor indices Empty sum, a sum with no terms Indefinite sum, the inverse of a finite difference Kronecker sum, an operation considered a kind
Sum
Indefinite integral
antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative
Antiderivative
Expression for sums of powers
falling factorials, and the behaviour of falling factorials under the indefinite sum. Interpreting the Stirling numbers of the second kind, { p + 1 k } {\displaystyle
Faulhaber's_formula
Danish mathematician (1885–1981)
Selsk. Mat. Fys. SKR. 5: 1–58. 1963. Nörlund–Rice integral Inge Lehmann Indefinite sum Bang, Thøger (1983). "Niels Erik Norlund. 26 October 1885-4 July 1981"
Niels_Erik_Nørlund
Summation method for hypergeometric terms
hypergeometric closed form for the indefinite sum of hypergeometric terms. It can happen that there is no such closed form, but that the sum over all n, or some particular
Gosper's_algorithm
Complex-differentiable part of a Maass wave function
discovered the relation with non-holomorphic modular forms, Lerch sums, and indefinite theta series. Zwegers showed, using the previous work of Watson and
Mock_modular_form
Discrete analog of a derivative
the forward difference operator, so then the umbral integral, is the indefinite sum or antidifference operator. Analogous to rules for finding the derivative
Finite_difference
Multi-dimensional generalization of triangle
1) in R5. An alternative coordinate system is given by taking the indefinite sum: s 0 = 0 s 1 = s 0 + t 0 = t 0 s 2 = s 1 + t 1 = t 0 + t 1 s 3 = s 2
Simplex
Incomplete gamma function – Types of special mathematical functions Indefinite sum – Inverse of a finite difference Integration using Euler's formula –
Lists_of_integrals
Equalities involving sums over the coefficients occurring in hypergeometric series
two types of sums over hypergeometric terms, the definite and indefinite sums. A definite sum is of the form ∑ k t k . {\displaystyle \sum _{k}t_{k}.}
Hypergeometric_identity
Operation in calculus
standard part of an infinite Riemann sum, based on the hyperreal number system. The notation for the indefinite integral was introduced by Gottfried Wilhelm
Integral
(Nabla operator) L [ y ] = ∑ y = Δ − 1 y {\displaystyle L[y]=\sum y=\Delta ^{-1}y} Indefinite sum operator (inverse operator of difference) L [ y ] = − ( p
List_of_mathematic_operators
English serial killer and rapist
other attacks on women. Napper was sentenced to indefinite detention at Broadmoor Hospital. In his summing up at the Old Bailey Mr Justice Griffiths Williams
Robert_Napper
Vector space in functional analysis
In mathematics, in the field of functional analysis, an indefinite inner product space ( K , ⟨ ⋅ , ⋅ ⟩ , J ) {\displaystyle (K,\langle \cdot ,\,\cdot \rangle
Indefinite inner product space
Indefinite_inner_product_space
Formulation of quantum mechanics
classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible
Path-integral_formulation
Branch of mathematics
concepts, the indefinite integral and the definite integral. The process of finding the value of an integral is called integration. The indefinite integral
Calculus
{\displaystyle f'(x)} is continuous. Mathematics portal List of integrals Indefinite sum Gamma function List of limits Reynolds, Robert; Stauffer, Allan (2020)
List_of_definite_integrals
Type of homogeneous polynomial of degree 2
words, it may take on zero values for some non-zero vectors of V. An indefinite quadratic form takes on both positive and negative values and is called
Definite_quadratic_form
Method for evaluating indefinite integrals
case of rational functions, as he showed that the indefinite integral of a rational function is the sum of a rational function and a finite number of constant
Risch_algorithm
meters Many languages have words expressing indefinite and fictitious numbers—inexact terms of indefinite size, used for comic effect, for exaggeration
List_of_numbers
Probability distribution
− Φ ( x ) {\displaystyle \Phi (-x)=1-\Phi (x)} . Its antiderivative (indefinite integral) can be expressed as follows: ∫ Φ ( x ) d x = x Φ ( x ) + φ (
Normal_distribution
2022 American reality television series
season but has yet to give any updates likely putting the series on an indefinite hiatus. On March 8, 2025, Zeus CEO Lemuel Plummer finally teased a possible
Bad_Boys_(TV_series)
Property of infinite series
{\textstyle \sum _{n=0}^{\infty }a_{n}} is said to converge conditionally if lim m → ∞ ∑ n = 0 m a n {\textstyle \lim _{m\rightarrow \infty }\,\sum _{n=0}^{m}a_{n}}
Conditional_convergence
Neil Armstrong's words on landing on the Moon
of Armstrong's Apollo 11 transmission do not provide evidence for the indefinite article "a" before "man", leading to some controversy about whether he
One_small_step
Property of a mathematical matrix
positive semi-definite and not negative semi-definite is sometimes called indefinite. Some authors use more general definitions of definiteness, permitting
Definite_matrix
Group of unitary matrices
points over various algebras. Analogous to the indefinite orthogonal groups, one can define an indefinite unitary group, by considering the transforms that
Unitary_group
Function with variable number of arguments
mathematics and in computer programming, a variadic function is a function of indefinite arity, i.e., one which accepts a variable number of arguments. Support
Variadic_function
American post-hardcore band
Highly influential on punk and alternative music, the band has been on an indefinite hiatus since 2003. After the hardcore punk group Minor Threat dissolved
Fugazi
series expansion is the expected k-th derivative, if k > 0, or (−k)th indefinite integral normalized by integration from θ = 0. The condition a0 = 0 here
Weyl_integral
Identity expressing an integral as a sum
_{0}^{1}x^{-x}\,dx&&=\sum _{n=1}^{\infty }n^{-n}\\&\int _{0}^{1}x^{x}\,dx&&=\sum _{n=1}^{\infty }(-1)^{n+1}n^{-n}=-\sum _{n=1}^{\infty }(-n)^{-n}\end{alignedat}}}
Sophomore's_dream
Study of Galois symmetry groups of differential fields
stated in the theorem. Intuitively, only elementary indefinite integrals can be expressed as the sum of a finite number of logarithms of simple functions
Differential_Galois_theory
Functions of an angle
these definitions result in simple expressions for the derivatives and indefinite integrals for the trigonometric functions. Thus, in settings beyond elementary
Trigonometric_functions
2025 video game
critics. A Nintendo Switch 2 release was announced but has been put on an indefinite pause with no future plans. Set six years after the events of the last
Borderlands_4
Basic proposition or assumption
the same reason. Instead, he proposed the existence of the apeiron, an indefinite substance from which all things are born and to which all things will
First_principle
Computer algebra system
and exponential functions. It can calculate symbolic antiderivatives ("indefinite integrals"), definite integrals, and limits. It can derive closed-form
Maxima_(software)
American punk rock band
decided to go on an indefinite hiatus and released the following statement on their official website: We've decided to take an indefinite break from Autopilot
Autopilot_Off
2020 film by Christopher Nolan
on HBO Go streaming platform on June 12, 2021, following the year-long indefinite closure of theaters in the country in response of a potential COVID-19
Tenet
complete list of integral functions, please see the list of integrals. Indefinite integrals are antiderivative functions. A constant (the constant of integration)
List of integrals of exponential functions
List_of_integrals_of_exponential_functions
Header file for C programs
library of the C programming language that allows functions to accept an indefinite number of arguments. It provides facilities for stepping through a list
Stdarg.h
Critical point on a surface graph which is not a local extremum
compute the function's Hessian matrix at that point: if the Hessian is indefinite, then that point is a saddle point. For example, the Hessian matrix of
Saddle_point
Solution to x*x + y*y + z*z = 3xyz
a x 2 + b x y + c y 2 {\displaystyle f(x,y)=ax^{2}+bxy+cy^{2}} is an indefinite binary quadratic form with real coefficients and discriminant D = b 2
Markov_number
Probability of shared birthdays
contains a section where the main characters, trapped underground for an indefinite amount of time, are celebrating a birthday and find themselves discussing
Birthday_problem
South African legal case
in the fact that, in Totoyi, the formula stipulated an indefinite period, during which indefinite amounts would be added, whereas in the second the formula
Totoyi_v_Ncuka
angle maximization problem Rolle's theorem Antiderivative/Indefinite integral Simplest rules Sum rule in integration Constant factor rule in integration
List_of_calculus_topics
Characters used to denote numbers in Chinese History of large numbers Indefinite and fictitious numbers Indian numbering system – Indian convention of
Names_of_large_numbers
Grammar of the Latin language
some tenses are formed from part of the verb sum "I am" added to a participle; for example, ductus sum "I was led" or ductūrus est "he is going to lead"
Latin_grammar
Number used for counting
concluded that it is "the power of the mind" which allows conceiving of the indefinite repetition of the same act. Leopold Kronecker summarized his belief as
Natural_number
Integral of the Gaussian function, equal to sqrt(π)
the methods of multivariable calculus. That is, there is no elementary indefinite integral for ∫ e − x 2 d x , {\displaystyle \int e^{-x^{2}}\,dx,} but
Gaussian_integral
Relationship between derivatives and integrals
calculus, states that for a continuous function f , an antiderivative or indefinite integral F can be obtained as the integral of f over an interval with
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Language of ancient Sumer and Babylon
romanized: eme-gir15, lit. 'native language') was the language of ancient Sumer. It is the oldest attested language, dating back to at least 3100 BC, perhaps
Sumerian_language
Swiss mathematician (1707–1783)
is the "exponent" of the genre (i.e. the sum of the exponents of 3 and 5) and 2m (where "m is an indefinite number, small or large, so long as the sounds
Leonhard_Euler
Transcendental single-variable function
classes of logarithmic and polylogarithmic integrals, both definite and indefinite. They also have numerous applications with regard to the summation of
Clausen_function
Topics referred to by the same term
orderly system World, the planet Earth, or the sum of human civilization everything, an English indefinite pronoun Everything (band), an American rock band
Everything_(disambiguation)
Highest velocity attainable by a falling object
through a fluid (air is the most common example). It is reached when the sum of the drag force (Fd) and the buoyancy is equal to the downward force of
Terminal_velocity
Mathematical function, denoted exp(x) or e^x
although being of very different nature. The exponential function converts sums to products: exp ( x + y ) = exp x ⋅ exp y {\displaystyle \exp(x+y)=\exp
Exponential_function
hydrogen atoms are bound into an atom, that atom's energy must be less than the sum of the energies of the separate hydrogen atoms. That lost energy, according
History_of_atomic_theory
1963 speech by U.S. President John F. Kennedy in West Berlin
incorrect to use an indefinite article before an indication of a person's origin, profession. As explained in the Duden-Grammatik: "Der indefinite Artikel wird
Ich_bin_ein_Berliner
West Germanic language
the three genders, between the nominative and oblique cases and between indefinite (weak) and definite (strong) forms. However, there is a lot of variation
Low_German
Indian activist (born 1937)
Minister within the ambit of the proposed lokpal's powers". Hazare began an "indefinite fast" on 5 April 2011 at Jantar Mantar in Delhi as part of the campaign
Anna_Hazare
Japanese rock band
Oricon number one Eleven Fire Crackers (2006), the band announced an indefinite hiatus in 2008. In May 2018, Ellegarden announced a reunion and held their
Ellegarden
Natural number
107, 109), at 110, the Mertens function reaches a low of −5. 110 is the sum of three consecutive squares, 110 = 5 2 + 6 2 + 7 2 {\displaystyle 110=5^{2}+6^{2}+7^{2}}
110_(number)
Short story by Poul Anderson
dominated by a massive computer, SUM, which claims to record the soul, and promises a resurrection at an indefinite future date. A harper—who alone remembers
Goat_Song_(novelette)
Mathematical concept
Greek philosopher. He used the word apeiron, which means "unbounded", "indefinite", and perhaps can be translated as "infinite". Aristotle (350 BC) distinguished
Infinity
British rock band (1990–2020)
release their 12th studio album in 2020. However, Anathema announced an indefinite hiatus on 22 September 2020. Daniel Cavanagh has announced he is working
Anathema_(band)
Short story by Jorge Luis Borges
"The Book of Sand", in which there is an infinite book (or book with an indefinite number of pages) rather than an infinite library. Moreover, the story's
The_Library_of_Babel
Matrix decomposition method
of non-zero elements on the diagonal D is exactly the rank of A. Some indefinite matrices for which no Cholesky decomposition exists have an LDL decomposition
Cholesky_decomposition
American musician and actress (born 1974)
eponymous debut, they released six more studio albums before going on indefinite hiatus in 2006. In a 2012 interview with DIY magazine, Brownstein said
Carrie_Brownstein
Integral using products instead of sums
A product integral is any product-based counterpart of the usual sum-based integral of calculus. The product integral was developed by the mathematician
Product_integral
Matrix with the same number of rows and columns
n×n-matrix is called positive-definite (respectively negative-definite; indefinite), if for all nonzero vectors x ∈ R n {\displaystyle x\in \mathbb {R} ^{n}}
Square_matrix
1943 paper proposing artificial neural networks
McCulloch–Pitts neurons. These neurons receive inputs, perform a weighted sum, and fire an output signal based on a threshold function. By connecting these
A Logical Calculus of the Ideas Immanent in Nervous Activity
A_Logical_Calculus_of_the_Ideas_Immanent_in_Nervous_Activity
Notation of differential calculus
for differentiation (and its opposite operation, antidifferentiation or indefinite integration) are listed below. The original notation employed by Gottfried
Notation_for_differentiation
Integral lattice of determinant 1 or –1
their non-existence has been proven for dimensions above 163,264. For indefinite lattices, the classification is easy to describe. Write Rm,n for the m + n
Unimodular_lattice
Theorem in probability theory
approximation error for all n (and hence the limiting rate of convergence for indefinite n sufficiently large) is bounded by the order of n−1/2. Calculated upper
Berry–Esseen_theorem
Infinite sum that is considered independently from any notion of convergence
[ X ] ] , {\displaystyle f=\sum _{n\geq 0}a_{n}X^{n}\in R[[X]],} we define its formal antiderivative or formal indefinite integral by D − 1 f = ∫ f
Formal_power_series
Function acting on function spaces
preserve properties, such as continuity. For example, differentiation and indefinite integration are linear operators; operators that are built from them are
Operator_(mathematics)
2024 studio album by Imagine Dragons
first release as a trio, due to drummer Daniel Platzman announcing an indefinite hiatus from the band in March 2023, later departing from the band in August
Loom_(Imagine_Dragons_album)
Technique in integral evaluation
forms. Before stating the result rigorously, consider a simple case using indefinite integrals. Compute ∫ ( 2 x 3 + 1 ) 7 ( x 2 ) d x . {\textstyle \int
Integration_by_substitution
Probability distribution
elementary probability courses, as a distribution with no well-defined (or "indefinite") moments. If we take an IID sample X 1 , X 2 , … {\displaystyle X_{1}
Cauchy_distribution
Canadian Christian rock band
DVD combo pack. After releasing the live album in 2017, TFK entered an indefinite hiatus to focus more on their families, with Trevor McNevan working on
Thousand_Foot_Krutch
Double cover Lie group of the special orthogonal group
more details). For higher n, these isomorphisms disappear entirely. In indefinite signature, the spin group Spin ( p , q ) {\displaystyle {\text{Spin}}(p
Spin_group
Annual music festival
On February 25, 2013, the Sarnia Bayfest announced it was taking an indefinite hiatus as a result of high debt, increasing costs and stagnant sponsorships
Sarnia_Bayfest
Cuomo Prime Time—four days after the network initially placed him on indefinite suspension following the November 29 release of documents in the sexual
2021_in_American_television
2007 child death in London
place on 22 May 2009 at the Old Bailey. Connelly received a sentence of indefinite imprisonment for public protection, subject to a minimum term of five
Killing_of_Peter_Connelly
Mathematical form
X k {\displaystyle {\biggl (}\sum _{i=0}^{n}a_{i}X^{i}{\biggr )}\cdot {\biggl (}\sum _{j=0}^{m}b_{j}X^{j}{\biggr )}=\sum _{k=0}^{n+m}c_{k}X^{k}} with c
Product_(mathematics)
Types of special mathematical functions
{\displaystyle \gamma (s,x)=\sum _{k=0}^{\infty }{\frac {x^{s}e^{-x}x^{k}}{s(s+1)\cdots (s+k)}}=x^{s}\,\Gamma (s)\,e^{-x}\sum _{k=0}^{\infty }{\frac {x^{k}}{\Gamma
Incomplete_gamma_function
Concept in game theory
behavior of all the other players. Although the hierarchy of types could be indefinite, the benefits of higher levels would decrease substantially while incurring
Focal_point_(game_theory)
Owner of a rented building, land or real estate
the lease termination, the lease may automatically transition into an indefinite-term agreement, complicating eviction procedures further. Security deposits
Landlord
Verb that is active in meaning but takes its form from a different voice
was a compound verb just like the passive voice of regular verbs (factus sum 'I have been done'). Old Irish has a substantial number of deponent verbs
Deponent_verb
Islamist Palestinian political and paramilitary organization
signal a recognition of Israel. A Hamas official said that having an indefinite truce with Israel doesn't contradict Hamas's lack of recognition of Israel
Hamas
Data transformation of statistics into rank
Moffat, Alistair; Zobel, Justin (November 2010). "A Similarity Measure for Indefinite Rankings". ACM Transactions on Information Systems. 28 (4): 1–38. doi:10
Ranking_(statistics)
Indefinite quadratic forms in > 4 variables over the rationals nontrivially represent 0
In number theory, Meyer's theorem on quadratic forms states that an indefinite quadratic form Q in five or more variables over the field of rational numbers
Meyer's_theorem
Cast of neo-Western crime media franchise
for Skyler's infidelity with Ted), resulting in him being placed on an indefinite sabbatical. In Season 5, she has been promoted to principal. Mrs. Nguyen
List of characters in the Breaking Bad franchise
List_of_characters_in_the_Breaking_Bad_franchise
Military base of the United States Navy
naval base. Since 1974, the U.S. has paid the Cuban government an annual sum equivalent to $4,085 in 1934 dollars (approximately $98,314 in 2025) to lease
Guantanamo_Bay_Naval_Base
Old English riddle
support strang strang adjective strong, powerful, bold, brave, severe sumes sum indefinite pronoun a certain one, someone, something swealg swelgan strong verb
Exeter_Book_Riddle_47
over his recent behavior and placing the errant creative director on an indefinite leave of absence. In Season 7, after Roger's urging, Cooper is willing
List_of_Mad_Men_characters
Multivariate generalization of the gamma function
{1-p}{2}})G(a+1-{\frac {p}{2}})}}} Where G is the Barnes G-function, the indefinite product of the Gamma function. The function is derived by Anderson from
Multivariate_gamma_function
is universal if it has dimension at least 4. One can conclude that all indefinite forms of dimension at least 4 over Q {\displaystyle \mathbb {Q} } are
Universal_quadratic_form
INDEFINITE SUM
INDEFINITE SUM
Boy/Male
Hindi
Infinite.
Boy/Male
Indian
Infinite visionary
Girl/Female
Indian, Telugu
Infinite
Boy/Male
Tamil
Infinite, Endless
Girl/Female
Hindu, Indian, Marathi
Infinite; Matchless
Boy/Male
Hindu
Infinite, Endless
Boy/Male
Tamil
Infinite visionary
Boy/Male
Japanese
Infinite; endless.
Boy/Male
Hindu, Indian, Marathi, Sanskrit
Infinite
Boy/Male
Hindu
Infinite, Endless
Girl/Female
Hindu, Indian
Infinite
Boy/Male
Tamil
Infinite, Endless
Boy/Male
Hindu
Infinite God
Boy/Male
Tamil
Infinite God
Boy/Male
Indian
Infinite.
Girl/Female
Tamil
Infinite, Divine
Girl/Female
Indian
Infinite, Divine
Girl/Female
Indian, Telugu
Infinite
Girl/Female
Hindu, Indian, Marathi
Infinite; Knowledge
Girl/Female
Hindi
Infinite.
INDEFINITE SUM
INDEFINITE SUM
INDEFINITE SUM
INDEFINITE SUM
INDEFINITE SUM
INDEFINITE SUM
INDEFINITE SUM