A

• Niels Abel: Abel polynomials - Abelian function - Abel–Gontscharoff interpolating polynomial
• Sir George Biddell Airy: Airy function
  Airy function
  In the physical sciences, the Airy function Ai is a special function named after the British astronomer George Biddell Airy...
  
  
• Waleed Al-Salam
  Waleed Al-Salam
  Waleed Al-Salam was a mathematician who introduced Al-Salam–Chihara polynomials, Al-Salam–Carlitz polynomials, q-Konhauser polynomials, and Al-Salam–Ismail polynomials....
  
   (1926–1996): Al-Salam polynomial
  Al-Salam–Ismail polynomials
  In mathematics, the Al-Salam–Ismail polynomials are a family of orthogonal polynomials introduced by ....
  
   - Al Salam–Carlitz polynomial - Al Salam–Chihara polynomial
• C. T. Anger: Anger–Weber function
• Kazuhiko Aomoto: Aomoto–Gel'fand hypergeometric function - Aomoto integral
• Paul Émile Appell
  Paul Émile Appell
  Paul Appell , also known as Paul Émile Appel, was a French mathematician and Rector of the University of Paris...
  
   (1855–1930): Appell hypergeometric series, Appell polynomial, Generalized Appell polynomials
• Richard Askey
  Richard Askey
  Richard Allen Askey is an American mathematician, known for his expertise in the area of special functions. The Askey–Wilson polynomials are an important schematic in organising the theory of special polynomials...
  
  : Askey–Wilson polynomial, Askey–Wilson function (with James A. Wilson
  James A. Wilson
  James Arthur Wilson is a mathematician working on special functions and orthogonal polynomials who introduced Wilson polynomials and Askey–Wilson polynomials and the Askey–Wilson beta integral.-References:*...
  
  )

B

• Ernest William Barnes
  Ernest William Barnes
  Ernest William Barnes FRS was an English mathematician and scientist who later became a theologian and bishop....
  
  : Barnes G-function
  Barnes G-function
  In mathematics, the Barnes G-function G is a function that is an extension of superfactorials to the complex numbers. It is related to the Gamma function, the K-function and the Glaisher-Kinkelin constant, and was named after mathematician Ernest William Barnes...
  
  
• E. T. Bell: Bell polynomials
  • Bender–Dunne polynomial
• Jacob Bernoulli: Bernoulli polynomial
• Friedrich Bessel
  Friedrich Bessel
  -References:* John Frederick William Herschel, A brief notice of the life, researches, and discoveries of Friedrich Wilhelm Bessel, London: Barclay, 1847 -External links:...
  
  : Bessel function
  Bessel function
  In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y of Bessel's differential equation:...
  
  , Bessel–Clifford function
• H. Blasius: Blasius functions
• R. P. Boas, R. C. Buck: Boas–Buck polynomial
  • Boehmer integral
• de Bruijn function
• Burchnall, Chaundy: Burchnall–Chaundy polynomial

C

• Leonard Carlitz
  Leonard Carlitz
  Leonard Carlitz was an American mathematician. Carlitz supervised 44 Doctorates at Duke University and published over 770 papers.- Chronology :* 1907 Born Philadelphia, PA, USA* 1927 BA, University of Pennsylvania...
  
  : Carlitz polynomial
• Arthur Cayley
  Arthur Cayley
  Arthur Cayley F.R.S. was a British mathematician. He helped found the modern British school of pure mathematics....
  
  , Capelli
  Alfredo Capelli
  Alfredo Capelli was an Italian mathematician who discovered Capelli's identity.Capelli graduated from the University of Rome in 1877, and moved to the University of Pavia where he worked as an assistant for Felice Casorati...
  
  : Cayley–Capelli operator
  • Celine's polynomial
  • Charlier polynomial
• Pafnuty Chebyshev
  Pafnuty Chebyshev
  Pafnuty Lvovich Chebyshev was a Russian mathematician. His name can be alternatively transliterated as Chebychev, Chebysheff, Chebyshov, Tschebyshev, Tchebycheff, or Tschebyscheff .-Early years:One of nine children, Chebyshev was born in the village of Okatovo in the district of Borovsk,...
  
  : Chebyshev polynomials
  Chebyshev polynomials
  In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivre's formula and which can be defined recursively. One usually distinguishes between Chebyshev polynomials of the first kind which are denoted Tn and...
  
  
• Christoffel, Darboux: Christoffel–Darboux relation
• Cyclotomic polynomial
  Cyclotomic polynomial
  In algebra, the nth cyclotomic polynomial, for any positive integer n, is the monic polynomial:\Phi_n = \prod_\omega \,where the product is over all nth primitive roots of unity ω in a field, i.e...
  
  s

D

• Dawson function
• Charles F. Dunkl: Dunkl operator
  Dunkl operator
  In mathematics, particularly the study of Lie groups, a Dunkl operator is a certain kind of mathematical operator, involving differential operators but also reflections in an underlying space....
  
  , Jacobi–Dunkl operator, Dunkl–Cherednik operator
  • Dickman–de Bruijn function

E

• Engel
  Friedrich Engel (mathematician)
  Friedrich Engel was a German mathematician.Engel was born in Lugau, Saxony, as the son of a Lutheran pastor. He attended the Universities of both Leipzig and Berlin, before receiving his doctorate from Leipzig in 1883.Engel studied under Felix Klein at Leipzig, and collaborated with Sophus Lie for...
  
  : Engel expansion
• Erdélyi Artúr: Erdelyi–Kober operator
• Leonhard Euler
  Leonhard Euler
  Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
  
  : Euler polynomial, Eulerian integral, Euler hypergeometric integral

F

• V. N. Faddeeva: Faddeeva function (also known as the complex error function; see error function
  Error function
  In mathematics, the error function is a special function of sigmoid shape which occurs in probability, statistics and partial differential equations...
  
  )

G

• C. F. Gauss: Gaussian polynomial, Gaussian distribution, etc.
• Leopold Bernhard Gegenbauer: Gegenbauer polynomials
  Gegenbauer polynomials
  In mathematics, Gegenbauer polynomials or ultraspherical polynomials C are orthogonal polynomials on the interval [−1,1] with respect to the weight function α–1/2. They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials...
  
  
  • Gottlieb polynomial
  • Gould polynomial
• Christoph Gudermann
  Christoph Gudermann
  Christoph Gudermann was born in Vienenburg. He was the son of a school teacher and became a teacher himself after studying at the University of Göttingen, where his advisor was Karl Friedrich Gauss...
  
  : Gudermannian function

H

• Wolfgang Hahn: Hahn polynomial, (with H. Exton) Hahn–Exton Bessel function
• Philip Hall
  Philip Hall
  Philip Hall FRS , was an English mathematician.His major work was on group theory, notably on finite groups and solvable groups.-Biography:...
  
  : Hall polynomial
  Hall polynomial
  In mathematics the Hall algebra is an associative algebra with a basis corresponding to isomorphism classes of finite abelian p-groups. It was first discussed by E. but forgotten until it was rediscovered by , both of whom published no more than brief summaries of their work. The Hall polynomials...
  
  , Hall–Littlewood polynomial
  Hall–Littlewood polynomial
  In mathematics, the Hall–Littlewood polynomials are symmetric functions depending on a parameter t and a partition λ. They are Schur functions when t is 0 and monomial symmetric functions when t is 1 and are special cases of Macdonald polynomials.They were first defined indirectly by ...
  
  
• Hermann Hankel
  Hermann Hankel
  Hermann Hankel was a German mathematician who was born in Halle, Germany and died in Schramberg , Imperial Germany....
  
  : Hankel function
• Heine
  Heine
  Heine is a German family name. The name comes from "Heinrich" or the Hebrew "Chayyim" . When mentioned without a first name it usually refers ti the poet Heinrich Heine...
  
  : Heine functions
• Charles Hermite
  Charles Hermite
  Charles Hermite was a French mathematician who did research on number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra....
  
  : Hermite polynomials
  Hermite polynomials
  In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence that arise in probability, such as the Edgeworth series; in combinatorics, as an example of an Appell sequence, obeying the umbral calculus; in numerical analysis as Gaussian quadrature; and in physics, where...
  
  
• Karl L. W. M. Heun (1859 – 1929): Heun's equation
  Heun's equation
  In mathematics, the local Heun function H⁢ℓ is the solution of Heun's differential equation that is holomorphic and 1 at the singular point z = 0...
  
  
• J. Horn: Horn hypergeometric series
• Adolf Hurwitz
  Adolf Hurwitz
  Adolf Hurwitz was a German mathematician.-Early life:He was born to a Jewish family in Hildesheim, former Kingdom of Hannover, now Lower Saxony, Germany, and died in Zürich, in Switzerland. Family records indicate that he had siblings and cousins, but their names have yet to be confirmed...
  
  : Hurwitz zeta-function

J

• Henry Jack
  Henry Jack
  Henry Jack was a Scottish mathematician at University College Dundee. The Jack polynomials are named after him. His research dealt with the development of analytic methods to evaluate certain integrals over matrix spaces. His most famous paper relates his integrals to classes of symmetric...
  
   (1917–1978) Dundee: Jack polynomial
• F. H. Jackson
  F. H. Jackson
  The Reverend Frank Hilton Jackson was an English clergyman and mathematician who worked on basic hypergeometric series. He introduced several q-analogs such as the...
  
  : Jackson derivative Jackson integral
  Jackson integral
  In q-analog theory, the Jackson integral series in the theory of special functions that expresses the operation inverse to q-differentiation.The Jackson integral was introduced by Frank Hilton Jackson.- Definition :...
  
  
• Carl Gustav Jakob Jacobi
  Carl Gustav Jakob Jacobi
  Carl Gustav Jacob Jacobi was a German mathematician, widely considered to be the most inspiring teacher of his time and is considered one of the greatest mathematicians of his generation.-Biography:...
  
  : Jacobi polynomial

K

• Joseph Marie Kampe de Feriet (1893–1982): Kampe de Feriet hypergeometric series
• David Kazhdan
  David Kazhdan
  David Kazhdan or Každan, Kazhdan, formerly named Dmitry Aleksandrovich Kazhdan , is a Soviet and Israeli mathematician known for work in representation theory.-Life:...
  
  , George Lusztig: Kazhdan–Lusztig polynomial
  Kazhdan–Lusztig polynomial
  In representation theory, a Kazhdan–Lusztig polynomial Py,w is a member of a family of integral polynomials introduced by . They are indexed by pairs of elements y, w of a Coxeter group W, which can in particular be the Weyl group of a Lie group.- Motivation and history:In the spring of 1978...
  
  
• Lord Kelvin: Kelvin function
  • Kibble–Slepian formula
    Kibble–Slepian formula
    In mathematics, the Kibble–Slepian formula, introduced by and , expresses the exponential of a quadratic form in terms of Hermite polynomials, generalizing Mehler's formula to several variables....
    
    
• Kirchhoff
  Gustav Kirchhoff
  Gustav Robert Kirchhoff was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects...
  
  : Kirchhoff polynomial
• Tom H. Koornwinder
  Tom H. Koornwinder
  Tom H. Koornwinder is a Dutch mathematician at the Korteweg-de Vries Institute of Mathematics who introduced Koornwinder polynomials.-References:***...
  
  : Koornwinder polynomial
  • Kostka polynomial
    Kostka polynomial
    In mathematics, a Kostka polynomial or Kostka–Foulkes polynomial Kλμ, named after Carl Kostka, is a polynomial in two variables with non-negative integer coefficients depending on two partitions λ and μ...
    
    , Kostka–Foulkes polynomial
• Mikhail Kravchuk
  Mikhail Kravchuk
  Mikhail Filippovich Kravchuk, also Krawtchouk was a Ukrainian mathematician who, despite his early death, was the author of around 180 articles on mathematics....
  
  : Kravchuk polynomial

L

• Edmond Laguerre
  Edmond Laguerre
  Edmond Nicolas Laguerre was a French mathematician, a member of the Académie française . His main works were in the areas of geometry and complex analysis. He also investigated orthogonal polynomials...
  
  : Laguerre polynomials
  Laguerre polynomials
  In mathematics, the Laguerre polynomials, named after Edmond Laguerre ,are the canonical solutions of Laguerre's equation:x\,y + \,y' + n\,y = 0\,which is a second-order linear differential equation....
  
  
• Gabriel Lamé
  Gabriel Lamé
  Gabriel Léon Jean Baptiste Lamé was a French mathematician.-Biography:Lamé was born in Tours, in today's département of Indre-et-Loire....
  
  : Lamé polynomial
• G. Lauricella Lauricella-Saran: Lauricella hypergeometric series
• Adrien-Marie Legendre
  Adrien-Marie Legendre
  Adrien-Marie Legendre was a French mathematician.The Moon crater Legendre is named after him.- Life :...
  
  : Legendre polynomials
• Eugen Cornelius Joseph von Lommel (1837–1899), physicist: Lommel polynomial, Lommel function, Lommel–Weber function

M

• Ian G. Macdonald
  Ian G. Macdonald
  Ian Grant Macdonald is a British mathematician known for his contributions to symmetric functions, special functions, Lie algebra theory and other aspects of algebraic combinatorics ....
  
  : Macdonald polynomial
  Macdonald polynomial
  In mathematics, Macdonald polynomials Pλ are a family of orthogonal polynomials in several variables, introduced by...
  
  , Macdonald–Kostka polynomial, Macdonald spherical function
  • Mahler polynomial
    Mahler polynomial
    In mathematics, the Mahler polynomials gn are polynomials introduced by in his work on the zeros of the incomplete gamma function.Mahler polynomials are given by the generating function\displaystyle \sum g_nt^n/n! = \exp...
    
    
  • Maitland function
• Emile Léonard Mathieu
  Émile Léonard Mathieu
  Émile Léonard Mathieu was a French mathematician. He is most famous for his work in group theory and mathematical physics. He has given his name to the Mathieu functions, Mathieu groups and Mathieu transformation...
  
  : Mathieu function
  Mathieu function
  In mathematics, the Mathieu functions are certain special functions useful for treating a variety of problems in applied mathematics, including*vibrating elliptical drumheads,*quadrupoles mass filters and quadrupole ion traps for mass spectrometry...
  
  
• F. G. Mehler, student of Dirichlet (Ferdinand): Mehler's formula, Mehler–Fock formula, Mehler–Heine formula
  Mehler–Heine formula
  In mathematics, the Mehler–Heine formula introduced by and describes the asymptotic behavior of the Legendre polynomials as the index tends to infinity, near the edges of the support of the weight. There are generalizations to other classical orthogonal polynomials, which are also called the...
  
  , Meier function
  Meier function
  In mathematics, Meier function might refer to:*Kaplan–Meier estimator*Meijer G-function...
  
  
  • Meijer G-function
    Meijer G-Function
    In mathematics, the G-function was introduced by as a very general function intended to include most of the known special functions as particular cases. This was not the only attempt of its kind: the generalized hypergeometric function and the MacRobert E-function had the same aim, but Meijer's...
    
    
• Josef Meixner
  Josef Meixner
  Josef Meixner was a German theoretical physicist known for his work on the physics of deformable bodies, thermodynamics, statistical mechanics, Meixner polynomials, Meixner-Pollaczek polynomials, and spheroidal wave functions.-Education:Meixner began his studies in theoretical physics with Arnold...
  
  : Meixner polynomial, Meixner-Pollaczek polynomial
• Mittag-Leffler: Mittag-Leffler polynomials
  • Mott polynomial

P

• Paul Painlevé
  Paul Painlevé
  Paul Painlevé was a French mathematician and politician. He served twice as Prime Minister of the Third Republic: 12 September – 13 November 1917 and 17 April – 22 November 1925.-Early life:Painlevé was born in Paris....
  
  : Painlevé function, Painlevé transcendents
  Painlevé transcendents
  In mathematics, Painlevé transcendents are solutions to certain nonlinear second-order ordinary differential equations in the complex plane with the Painlevé property , but which are not generally solvable in terms of elementary functions...
  
  
• Poisson–Charlier polynomial
• Pollaczek polynomial

R

• Giulio Racah: Racah polynomial
• Jacopo Riccati
  Jacopo Riccati
  Jacopo Francesco Riccati was an Italian mathematician, born in Venice. He is now remembered for the Riccati equation. He died in Treviso in 1754.-Education:...
  
  : Riccati–Bessel function
• Bernhard Riemann
  Bernhard Riemann
  Georg Friedrich Bernhard Riemann was an influential German mathematician who made lasting contributions to analysis and differential geometry, some of them enabling the later development of general relativity....
  
  : Riemann zeta-function
• Olinde Rodrigues
  Olinde Rodrigues
  Benjamin Olinde Rodrigues , more commonly known as Olinde Rodrigues, was a French banker, mathematician, and social reformer.Rodrigues was born into a well-to-do Sephardi Jewish family in Bordeaux....
  
  : Rodrigues formula
• Leonard James Rogers
  Leonard James Rogers
  Leonard James Rogers FRS was a British mathematician who was the first to discover the Rogers-Ramanujan identity and Hölder's inequality, and who introduced Rogers polynomials...
  
  : Rogers–Askey–Ismail polynomial, Rogers–Ramanujan identity, Rogers–Szegö polynomial

S

• • Schubert polynomial
    Schubert polynomial
    In mathematics, Schubert polynomials are generalizations of Schur polynomials that represent cohomology classes of Schubert cycles in flag varieties.They were introduced by and are named after Hermann Schubert.-Background:...
    
    
• Issai Schur
  Issai Schur
  Issai Schur was a mathematician who worked in Germany for most of his life. He studied at Berlin...
  
  : Schur polynomial
  Schur polynomial
  In mathematics, Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the elementary symmetric polynomials and the complete homogeneous symmetric polynomials. In representation theory they are the characters of...
  
  
• Atle Selberg
  Atle Selberg
  Atle Selberg was a Norwegian mathematician known for his work in analytic number theory, and in the theory of automorphic forms, in particular bringing them into relation with spectral theory...
  
  : Selberg integral
  • Sheffer polynomial
  • Slater's identities
• Thomas Joannes Stieltjes
  Thomas Joannes Stieltjes
  Thomas Joannes Stieltjes was a Dutch mathematician. He was born in Zwolle and died in Toulouse, France. He was a pioneer in the field of moment problems and contributed to the study of continued fractions....
  
  : Stieltjes polynomial
  Stieltjes polynomial
  In mathematics, the Heine–Stieltjes polynomials or Stieltjes polynomials, introduced by , are polynomial solutions of a second-order Fuchsian equation, a differential equation all of whose singularities are regular...
  
  , Stieltjes–Wigert polynomials
  • Stromgen function
• Hermann Struve
  Hermann Struve
  Karl Hermann Struve was a Russian astronomer. In Russian, his name is sometimes given as German Ottovich Struve or German Ottonovich Struve ....
  
  : Struve function

W

• • Wall polynomial
    Wall polynomial
    In mathematics, a Wall polynomial is a polynomial studied by in his work on conjugacy classes in classical groups, and named by ....
    
    
• Wangerein: Wangerein functions
  • Weber function
• Louis Weisner
  Louis Weisner
  Louis Weisner was a Canadian mathematician at the University of New Brunswick who introduced Weisner's method.-References:*...
  
  : Weisner's method
  Weisner's method
  In mathematics, Weisner's method is a method for finding generating functions for special functions using representation theory of Lie groups and Lie algebras, introduced by . It includes Truesdall's method as a special case, and is essentially the same as Rainville's method....
  
  
• E. T. Whittaker
  E. T. Whittaker
  Edmund Taylor Whittaker FRS FRSE was an English mathematician who contributed widely to applied mathematics, mathematical physics and the theory of special functions. He had a particular interest in numerical analysis, but also worked on celestial mechanics and the history of physics...
  
  : Whittaker function
  Whittaker function
  In mathematics, a Whittaker function is a special solution of Whittaker's equation, a modified form of the confluent hypergeometric equation introduced by to make the formulas involving the solutions more symmetric...
  
  
• Wilson polynomial