mathematics, the Bateman polynomials are a family Fn of orthogonal polynomials introduced by Harry Bateman (1933). The Bateman–Pasternack polynomials are a generalization...

theory, the Bateman–Horn conjecture is a statement concerning the frequency of prime numbers among the values of a system of polynomials, named after...

The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)}...

Harry Bateman FRS (29 May 1882 – 21 January 1946) was an English mathematician with a specialty in differential equations of mathematical physics. With...

^{7}-x^{6}-x^{5}+x^{2}+x+1.\end{aligned}}} The cyclotomic polynomials are monic polynomials with integer coefficients that are irreducible over the field...

numerical polynomials.[citation needed] The K-theory of BU(n) is numerical (symmetric) polynomials. The Hilbert polynomial of a polynomial ring in k + 1...

polynomials, Jacobi polynomials and Bateman polynomials as special cases. Fasenmyer, Mary Celine (1947), "Some generalized hypergeometric polynomials", Bulletin...

second condition also fails for the polynomials reducible over the rationals. For example, the integer-valued polynomial P ( x ) = ( 1 / 12 ) ⋅ x 4 + ( 11...

Korteweg-de Vries Institute for Mathematics who introduced Koornwinder polynomials. Askey–Bateman project Curriculum Vitae home page Tom H. Koornwinder at the Mathematics...

the continuous Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials. They are defined in...

(eds.). "The Askey-Bateman Project" (PDF). OP-SF NET: The Electronic News Net of the SIAM Activity Group on Orthogonal Polynomials and Special Functions...

systems of polynomials and the New Mersenne conjecture relating the occurrences of Mersenne primes and Wagstaff primes. Born in Philadelphia, Bateman received...

spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler's prime-generating polynomial x2 − x + 41, are believed to produce...

well-approximated by polynomials on [ − 1 , 1 ] {\displaystyle [-1,1]} , the associated orthogonal polynomials are Legendre polynomials, denoted by Pn(x)...

polynomial, and on the Hardy–Littlewood conjectures and Dickson's conjecture for multiple linear polynomials. It is in turn extended by the Bateman–Horn...

to be attained through cyclotomic polynomials. Cyclotomic polynomials cannot close this gap by a result of Bateman that states for every ε > 0 {\displaystyle...

Mittag-Leffler polynomials are the polynomials gn(x) or Mn(x) studied by Mittag-Leffler (1891). Mn(x) is a special case of the Meixner polynomial Mn(x;b,c)...

Hardy–Littlewood conjecture. The Bateman–Horn conjecture generalizes the first Hardy–Littlewood conjecture to polynomials of degree higher than 1. Aletheia-Zomlefer...

In mathematics, the Shapiro polynomials are a sequence of polynomials which were first studied by Harold S. Shapiro in 1951 when considering the magnitude...

Erdélyi was a leading expert on special functions, particularly orthogonal polynomials and hypergeometric functions. He was born Arthur Diamant in Budapest...

random walk polynomials (also known as the Askey–Ismail polynomials), the Al-Salam–Ismail polynomials, and the Chihara–Ismail polynomials. Ismail also...

regarding Bernoulli numbers Carlitz wrote about Bessel polynomials He introduced Al-Salam–Carlitz polynomials. Carlitz' identity for bicentric quadrilaterals...

Kramers–Pasternack recursion relations for the fine structure and Bateman–Pasternack polynomials are also named after him. Pasternack graduated from University...

orthogonal polynomials of ( q {\displaystyle q} -)hypergeometric type into a hierarchy. The Askey–Gasper inequality for Jacobi polynomials is essential...

Urbana-Champaign in 1972, officially under the supervision of Paul T. Bateman, but his de facto adviser was Paul Erdős.[citation needed] He was on the...

formulating the Bateman–Horn conjecture with Paul T. Bateman on the density of prime number values generated by systems of polynomials. His books Matrix...

some special cases solutions can be expressed in terms of polynomials called Lamé polynomials. Lamé's equation is d 2 y d x 2 + ( A + B ℘ ( x ) ) y = 0...

the sine integral, logarithmic integral Hermite polynomials Incomplete gamma function Laguerre polynomials Parabolic cylinder function (or Weber function)...

other number-theoretic conjectures such as the Bunyakovsky conjecture and Bateman–Horn conjecture. One example of near-square primes are Fermat primes. Henryk...

{}_{1}F_{1}(-n;b;z)} is a polynomial. Up to constant factors, these are the Laguerre polynomials. This implies Hermite polynomials can be expressed in terms...