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# Special functions

Select from the following:
Gamma function

Beta function

Bernoulli and Euler numbers

Bessel functions of the first and second
kind. Bessel's differential equation. Hankel functions.
Modified Bessel functions. Recurrence formulas.

Legendre functions of the first and second
kind. Legendre differential equation. Legendre polynomials.
Recurrence formulas. Generating function. Associated
Legendre functions

Hermite polynomials. Hermite's differential
equation. Generating function. Recurrence formulas.

Laguerre Polynomials. Laguerre differential
equation. Recurrence formulas. Generating function.
Associated Laguerre polynomials.

Chebyshev polynomials of the first and second
kind. Chebyshev's differential equation. Recurrence formulas.
Generating function.

Hypergeometric functions. Gauss hypergeometric
differential equation. Confluent hypergeometric differential
equation.

Elliptic integrals of the first, second and
third kind. Jacobian elliptic functions. Identities,
formulas, series expansions, derivatives, integrals.

Error and complementary error functions.
Exponential integral. Sine and cosine integrals. Fresnel
sine and cosine integrals.

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