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Family of solutions to related differential equations
Bessel functions are a class of special functions that commonly appear in problems involving wave motion, heat conduction, and other physical phenomena
Bessel_function
Topics referred to by the same term
Bessel may refer to: Bessel beam Bessel ellipsoid Bessel function in mathematics Bessel's inequality in mathematics Bessel's correction in statistics Bessel
Bessel
Mathematical potential
In mathematics, the Bessel potential is a potential (named after Friedrich Wilhelm Bessel) similar to the Riesz potential but with better decay properties
Bessel_potential
Non-diffractive wave
A Bessel beam is a wave whose amplitude is described by a Bessel function of the first kind. Electromagnetic, acoustic, gravitational, and matter waves
Bessel_beam
German astronomer and mathematician (1784–1846)
Friedrich Wilhelm Bessel (German: [ˈbɛsl̩]; 22 July 1784 – 17 March 1846) was a German astronomer, mathematician, physicist, and geodesist. He was the
Friedrich_Wilhelm_Bessel
Dutch psychiatrist, researcher and educator (born 1943)
Bessel van der Kolk (Dutch: [vɑn dɛr kɔlk]; born 8 July 1943) is a Boston-based Dutch-American psychiatrist, author, researcher and educator. Since the
Bessel_van_der_Kolk
Mathematics concept
In mathematics, the Bessel polynomials are an orthogonal sequence of polynomials. There are a number of different but closely related definitions. The
Bessel_polynomials
Type of analog linear filter in electronics
In electronics and signal processing, a Bessel filter is a type of analog linear filter with a maximally flat group delay (i.e., maximally linear phase
Bessel_filter
In mathematics, the Bessel–Maitland function, or Wright generalized Bessel function, is a generalization of the Bessel function, introduced by Edward Maitland
Bessel–Maitland_function
Mathematical operation
f(r) as the weighted sum of an infinite number of Bessel functions of the first kind Jν(kr). The Bessel functions in the sum are all of the same order ν
Hankel_transform
Correction for sample variance bias
In statistics, Bessel's correction is the use of n − 1 instead of n in the formula for the sample variance and sample standard deviation, where n is the
Bessel's_correction
2014 book by Bessel van der Kolk
Score: Brain, Mind, and Body in the Healing of Trauma is a 2014 book by Bessel van der Kolk about the purported effects of psychological trauma. The book
The_Body_Keeps_the_Score
Mathematical process for stochastic differential equations
In mathematics, a Bessel process, named after Friedrich Bessel. The n-dimensional Bessel process is the solution to the stochastic differential equation
Bessel_process
Special lens with a conical surface
generated. It can be used to turn a Gaussian beam into a non-diffractive Bessel-like beam. Axicons were first proposed in 1954 by John McLeod. Axicons are
Axicon
In mathematics, a Jackson q-Bessel function (or basic Bessel function) is one of the three q-analogs of the Bessel function introduced by Jackson (1906a
Jackson_q-Bessel_function
Infinite series of Bessel functions
Fourier–Bessel series is a particular kind of generalized Fourier series (an infinite series expansion on a finite interval) based on Bessel functions
Fourier–Bessel_series
V. Bessel and Co. was a musical firm founded in 1869 in St Petersburg by Vasily Vasil’yevich Bessel (1843–1907). His brother N. V. Bessel was a co-owner
V._Bessel_and_Co.
Dutch businessman and chess organiser
Bessel Kok (born 13 December 1941 in Hilversum) is a Dutch businessman and chess organiser living in Prague. He has served in top management positions
Bessel_Kok
Reference ellipsoid in geodesy
The Bessel ellipsoid (or Bessel 1841) is an important reference ellipsoid of geodesy. It is currently used by several countries for their national geodetic
Bessel_ellipsoid
Headland of Barentsøya, Svalbard
Kapp Bessels is a headland at Barentsøya, Svalbard. It is located at the northeastern coast of the island, and east of the glacier of Besselsbreen. The
Kapp_Bessels
Theorem on orthonormal sequences
In mathematics, especially functional analysis, Bessel's inequality is a statement about the coefficients of an element x {\displaystyle x} in a Hilbert
Bessel's_inequality
In mathematical analysis, the Bessel–Clifford function, named after Friedrich Bessel and William Kingdon Clifford, is an entire function of two complex
Bessel–Clifford_function
British historian
Richard Bessel FRHistS is professor of twentieth century history at the University of York and a member of the editorial boards of German History and History
Richard_Bessel
Used in finite impulse response filter design and spectral analysis
The Kaiser window, also known as the Kaiser–Bessel window, was developed by James Kaiser at Bell Laboratories. It is a one-parameter family of window functions
Kaiser_window
Main-belt asteroid
1552 Bessel (provisional designation 1938 DE1) is a stony Eoan asteroid from the outer regions of the asteroid belt, approximately 18 kilometers in diameter
1552_Bessel
Void between celestial bodies
the distance to a nearby star in 1838 by the German astronomer Friedrich Bessel. He showed that the star system 61 Cygni had a parallax of just 0.31 arcseconds
Outer_space
German mathematician and historian of mathematics
Erich Bessel-Hagen (12 September 1898 in Charlottenburg – 29 March 1946 in Bonn) was a German mathematician and a historian of mathematics. Erich Paul
Erich_Bessel-Hagen
Crater on the Moon
Bessel is a small lunar impact crater that is located in the southern half of the Mare Serenitatis. Despite its small size, this is the largest crater
Bessel_(crater)
Vector space of functions in mathematics
{F}}f\right]\in L^{p}(\mathbb {R} ^{n})\right\}} are called Bessel potential spaces (named after Friedrich Bessel). They are Banach spaces in general and Hilbert
Sobolev_space
Support points minimising bending of beams
linear, rather than angular, motion of the ends. The Bessel points (after Friedrich Wilhelm Bessel) are the points at which the length of the beam is maximized
Airy_points
In mathematics, the Hahn–Exton q-Bessel function or the third Jackson q-Bessel function is a q-analog of the Bessel function, and satisfies the Hahn-Exton
Hahn–Exton_q-Bessel_function
German physicist
Carl Ernst Bessel Hagen (who published under the name Ernst Hagen; 31 January 1851 – 15 January 1923) was a German applied and experimental physicist.
Ernst_Bessel_Hagen
incomplete Bessel functions are types of special functions which act as a type of extension from the complete-type of Bessel functions. The incomplete Bessel functions
Incomplete_Bessel_functions
Function used in signal processing
the DPSS windows: The Kaiser, or Kaiser–Bessel, window is a simple approximation of the DPSS window using Bessel functions, discovered by James Kaiser.
Window_function
1927 film directed by Richard Oswald
The Transformation of Dr. Bessel (German: Dr. Bessels Verwandlung) is a 1927 German silent film directed by Richard Oswald and starring Jakob Tiedtke
The Transformation of Dr. Bessel
The_Transformation_of_Dr._Bessel
Binary star system in the Cygnus constellation
motion was first demonstrated by Giuseppe Piazzi in 1804. In 1838, Friedrich Bessel measured its distance from Earth at about 10.4 light-years, very close to
61_Cygni
Area of Sevenoaks, Kent, England
Bessels Green is a village now incorporated into the built-up area of Sevenoaks in Kent, England. It is on the north-western outskirts of Sevenoaks, in
Bessels_Green
German Benedictine abbot and historian
Johann Franz Bessel (in religion Gottfried; 5 September 1672, at Buchen, in the Grand Duchy of Baden – 22 January 1749 at Göttweig) was a German Benedictine
Johann_Franz_Bessel
Finds the sum of certain infinite series involving Bessel functions of the first kind
Newberger in 1982, finds the sum of certain infinite series involving Bessel functions Jα of the first kind. It states that if μ is any non-integer complex
Lerche–Newberger_sum_rule
Fjord in Greenland
Bessel Fjord is a fjord in northeastern Greenland. Administratively it belongs to the NE Greenland National Park area. The area around the mouth of this
Bessel_Fjord
German cargo ship
Bessel was a cargo ship that was built in 1925 as Sorrento by AG Weser, Bremen for German owners. She was sold in 1926 and renamed Bessel. She was seized
MV_Bessel
Fjord in Greenland
Bessel Fjord (Danish: Bessels Fjord) is a fjord in northwestern Greenland. Administratively it belongs to the Avannaata municipality. Knud Rasmussen described
Bessel_Fjord,_NW_Greenland
Defunct secondary school in Könisberg, Germany
The Bessel-Oberrealschule was an Oberrealschule in Königsberg, Germany. The school was founded on 16 October 1865 as a Mittelschule, the Löbenichtische
Bessel-Oberrealschule
inequality Bessel potential Bessel potential spaces Bessel process Bessel beam Bessel filter Bessel function Bessel–Maitland function Incomplete Bessel functions
List of things named after Friedrich Bessel
List_of_things_named_after_Friedrich_Bessel
Scottish mathematician (1895–1944)
Birmingham University. He published "A certain type of Fourier-Bessel Series", a paper about Bessel functions, in 1924. Lumsden, who served during both World
Thomas_Lumsden
German zoologist and Arctic researcher
Emil Bessels (2 June 1847 – 30 March 1888) was a German zoologist, entomologist, physician, and Arctic researcher who is best known for his controversial
Emil_Bessels
Group of fraternal organizations
"Masonic U.S. Recognition of French Grand Lodges in the 20th century", Paul M. Bessel. retrieved 8 November 2013 Andrew Prescott, "The Old Charges Revisited"
Freemasonry
Distance that light travels in one year
measurement of the distance to a star other than the Sun, by Friedrich Bessel in 1838. The star was 61 Cygni, and he used a 160-millimetre (6.2 in) heliometre
Light-year
Continuous probability distribution
The variance-gamma distribution, generalized Laplace distribution or Bessel function distribution is a continuous probability distribution that is defined
Variance-gamma_distribution
Quantity in relativistic physics
identity represents the Lorentz factor in terms of an infinite series of Bessel functions: ∑ m = 1 ∞ ( J m − 1 2 ( m β ) + J m + 1 2 ( m β ) ) = 1 1 − β
Lorentz_factor
Way of evaluating continued fractions
continued fractions, and was originally devised to compute tables of spherical Bessel functions. The version often employed now is the simplification due to Thompson
Lentz's_algorithm
Reversible free swinging pendulum
weights until they were equal, was time-consuming and error-prone. Friedrich Bessel showed in 1826 that this was unnecessary. As long as the periods measured
Kater's_pendulum
The Friedrich Wilhelm Bessel Research Award (German: Friedrich Wilhelm Bessel-Forschungspreis) is a recognition from the Alexander von Humboldt Foundation
Friedrich Wilhelm Bessel Research Award
Friedrich_Wilhelm_Bessel_Research_Award
German polymath and scholar (1777–1855)
especially Wilhelm Olbers, Karl Ludwig Harding, and Friedrich Wilhelm Bessel, forming part of the informal group of astronomers known as the Celestial
Carl_Friedrich_Gauss
Mathematical integral transform
Macdonald function (modified Bessel function of the second kind) with imaginary index as its kernel. Unlike other Bessel function transforms, such as
Kontorovich–Lebedev_transform
Intergovernmental organisation
astronomers such as Friedrich Georg Wilhelm von Struve, Friedrich Wilhelm Bessel, Carl Friedrich Gauss and George Biddell Airy. A French scientific instrument
International Bureau of Weights and Measures
International_Bureau_of_Weights_and_Measures
Jewish nationalist movement
Zionist Thinking and the Creation of the Palestinian Refugee Problem". In Bessel, Richard; Haake, Claudia B. (eds.). Removing Peoples. Studies of the German
Zionism
Concept in differential equation mathematics
the hypergeometric equation, with three regular singular points, and the Bessel equation which is in a sense a limiting case, but where the analytic properties
Regular_singular_point
frequent weekly best seller of the year was The Body Keeps the Score by Bessel van der Kolk with 6 weeks at the top of the list, followed by Nobody's Girl
List of The New York Times number-one books of 2025
List_of_The_New_York_Times_number-one_books_of_2025
Geometric figure which approximates the Earth's shape
of data used in national surveys are several of special importance: the Bessel ellipsoid of 1841, the international Hayford ellipsoid of 1924, and (for
Earth_ellipsoid
function Airy function Bessel functions: Defined by a differential equation; useful in astronomy, electromagnetism, and mechanics. Bessel–Clifford function
List of mathematical functions
List_of_mathematical_functions
Algorithm in numerical analysis
originally developed to compute tables of the modified Bessel function but also applies to Bessel functions of the first kind and has other applications
Miller's_recurrence_algorithm
Bessel Opera-Ballet Млада Mlada 1872 1872 Krïlov Unfinished 1931 Muzgiz Opera Хованщина Khovanshchina 1872-06 1880 Mussorgsky Unfinished 1883 Bessel Opera
List of compositions by Modest Mussorgsky
List_of_compositions_by_Modest_Mussorgsky
Country in Central Europe
Central European University Press. p. 57. ISBN 978-963-9241-80-0. Richard Bessel; Dirk Schumann (2003). Life After Death: Approaches to a Cultural and Social
Hungary
Early American electromechanical computer (1944)
operators of the Mark I often called the machine "Bessy, the Bessel engine", after Bessel functions. The Mark I was disassembled in 1959; part of it was
Harvard_Mark_I
In mathematics, the q-Bessel polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A
Q-Bessel_polynomials
Electronic method of transmitting information with a carrier wave
wave carrier modulated by such a sinusoidal signal can be represented with Bessel functions; this provides the basis for a mathematical understanding of frequency
Frequency_modulation
Kind of microscopy
novel combination of techniques from Light sheet fluorescence microscopy, Bessel beam microscopy, and Super-resolution microscopy (specifically structured
Lattice light-sheet microscopy
Lattice_light-sheet_microscopy
French mathematician (1949–2014)
properties of semimartingales, Brownian motion and other Lévy processes, the Bessel processes, and their applications to mathematical finance. Yor was a professor
Marc_Yor
Post-World War II occupation of Germany
York: Basic Books. p. 7. ISBN 978-0-465-00337-2. Bessel 2010, chpt. 10. MacDonogh 2007, p. 7. Bessel 2010, chpt. 7. MacDonogh 2007, pp. 253–254. Gollancz
Allied-occupied_Germany
scholar in 2016. Wonpil Im was a recipient of the 2017 Friedrich Wilhelm Bessel Research Award in Bioinformatics and Theoretical Biology, awarded by the
Wonpil_Im
Political party in Germany
Richard Bessel & E.J. Feuchtwanger, Social Change and Political Development in Weimar Germany, Croom Helm, 1981, ISBN 085664921X, p. 147 Bessel & Feuchtwanger
Christian-National Peasants' and Farmers' Party
Christian-National_Peasants'_and_Farmers'_Party
New Zealand mountaineer (1919–2008)
J. C. Ross Abernethy Kane Hayes Polaris expedition Polaris C. F. Hall Bessels British Arctic Expedition HMS Alert Nares HMS Discovery Stephenson Markham
Edmund_Hillary
Village in Oxfordshire, England
Besselsleigh or Bessels Leigh is an English village and civil parish about 4+1⁄2 miles (7 km) southwest of Oxford. Besselsleigh was part of Berkshire
Besselsleigh
series of functions related to Bessel functions of half integral order. He created tables of what he called the Riccati-Bessel functions of the sines and
Arthur_Thomas_Doodson
Physicist
Technology in The Netherlands in 2022. He also received awards like the Bessel and Glenn Brown Awards, NASA iTech award and Mid-Career Award of International
Ivan_Smalyukh
C standard library header file
cyl_bessel_i computes regular modified cylindrical Bessel functions cyl_bessel_j computes cylindrical Bessel functions of the first kind cyl_bessel_k computes
C_mathematical_functions
Stable type of wave in physics
can be constructed as a non-monochromatic superposition of Bessel beams. Like ideal Bessel beams, ideal X-waves are mathematical constructs possessing
X-wave
French mathematician
G. de B. Robinson Award for a paper she coauthored that introduced free Bessel laws, a two-parameter family of generalizations of the free Poisson distribution
Mireille_Capitaine
a + b ) 2 {\displaystyle h=(a-b)^{2}/(a+b)^{2}} . Found by James Ivory, Bessel and Kummer, there are several equivalent ways to write it. The most concise
Perimeter_of_an_ellipse
Changed position of star vs background
years. Thomas Henderson, Friedrich Georg Wilhelm von Struve, and Friedrich Bessel made the first successful parallax measurements in 1832–1838, for the stars
Stellar_parallax
Korean mathematician
winner of the Friedrich Wilhelm Bessel Research Prize of the Alexander von Humboldt Foundation. "Friedrich Wilhelm Bessel-Forschungspreis für Prof'in. Dr
Mihyun_Kang
Song cycle by Modest Mussorgsky
with a new edition of the five songs of Series 1, were published by V. Bessel and Co. in 1908. 1. Ride on a Hobby Horse (D-flat major) A child relating
The_Nursery
Mathematical expression
improvement where it is least needed and Bessel brings its accuracy improvement where it is most needed. So, Bessel's formula could be said to be the most
Newton_polynomial
Electronic filters designed by the network synthesis method
response with frequency. The Bessel filter is named after Friedrich Bessel and the transfer function is based on Bessel polynomials. The driving point
Network_synthesis_filters
Crater on the Moon
formation is relatively isolated, being located to the northeast of the crater Bessel. It lies along a wrinkle ridge designated the Dorsum Azara. This crater
Sarabhai_(crater)
Type of optical device
are an infinite number of sidebands. There is a useful identity involving Bessel functions called the Jacobi–Anger expansion which can be used to derive
Electro-optic_modulator
Periodic comet
sketched by German astronomer Friedrich Wilhelm Bessel. Observations of streams of vapour prompted Bessel to propose that the jet forces of evaporating
Halley's_Comet
is a series expansion of analytic functions on a domain in terms of the Bessel function of the first kind. Kapteyn series are named after Willem Kapteyn
Kapteyn_series
Mathematical formula involving Bessel functions
involving Bessel functions found by Nikolay Yakovlevich Sonin. One such formula is the following integral formula involving a product of three Bessel functions:
Sonine_formula
polynomial q-binomial coefficient q-Pochhammer symbol q-Vandermonde identity q-Bessel polynomials q-Charlier polynomials q-Hahn polynomials q-Jacobi polynomials:
List_of_q-analogs
German suicides at the end of World War II
p. 160 Goeschel page 8 Goeschel page 150 Goeschel page 151–152 Bessel page 188 Bessel, Lüdtke, Weisbrod pages 78–79 Goeschel page 154 Goeschel page 157
Mass_suicides_in_Nazi_Germany
observations. Simon Schaffer wrote it "was the name given by astronomers after Bessel to the differences in measured transit times recorded by observers in the
Personal_equation
Sequence of differential equation solutions
{z}{2}}\right)^{-\alpha }J_{\alpha }(z),} where J α {\displaystyle J_{\alpha }} is a Bessel function of the first kind. See also:. Let ν = 4 n + 2 α + 2 {\displaystyle
Laguerre_polynomials
Document that proposed additions to the C++ standard library
(a+n)x^{n}}{\Gamma (c+n)n!}}} Regular modified cylindrical Bessel functions double cyl_bessel_i(double nu, double x); I ν ( x ) = i − ν J ν ( i x ) = ∑
C++_Technical_Report_1
Branch of Freemasonry fraternal organization
retrieved 25 November 2013 Paul M. Bessel, Exclusive Jurisdiction, 1998, retrieved 25 November 2013 "PHA Chart". bessel.org. Archived from the original on
Prince_Hall_Freemasonry
Class of ordinary differential equations
In mathematics and its applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form d d x [ p ( x ) d y
Sturm–Liouville_theory
19th-century American polar expedition
scientist Emil Bessels and meteorologist Frederick Meyer—both German—who looked down on what they perceived to be their unqualified commander. Bessels and Meyer
Polaris_expedition
Italian mountaineer, adventurer and explorer (born 1944)
J. C. Ross Abernethy Kane Hayes Polaris expedition Polaris C. F. Hall Bessels British Arctic Expedition HMS Alert Nares HMS Discovery Stephenson Markham
Reinhold_Messner
Swiss mathematician
in Die Theorie Der Bessel'schen Funktionen (A Treatise on the Theory of Bessel Functions) in two volumes (1898–1900). He was the author of very appreciated
Salomon_Eduard_Gubler
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