Bateman F

The Bateman polynomials $Z_n$ are defined by the formula $$Z_n(x) = {}_2F_2(-n,n+1;1;1;x),$$ where ${}_2F_2$ is a generalized hypergeometric function.

References

• Harry Bateman: Some Properties of a certain Set of Polynomials (1933) $3.$

Orthogonal polynomials

Laguerre $L_n^{(\alpha)}$

Bateman $F_n$

Bernoulli $B$

Bessel poly

Chebyshev T

Chebyshev U

Dickson

Euler $E$

Gegenbauer $C$

Hermite (phys)

Hermite (prob)

Jacobi $P^{(\alpha,\beta)}$

Laguerre $L$

Legendre $P$

Bernoulli $B$

Chebyshev $T$

Fibonacci

Lucas