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Special functions

Bessel functions
Beta function
Binomial function
Cosine function
Dedekind eta function
Dirichlet eta function
Error function
Jacobi elliptic functions
Lambert $W$ Function
Logarithm
$q$-Bessel function
$q$-Beta function
$q$-Gamma function
Gamma function
Generalized hypergeometric function ${}_pF_q$
Pochhammer symbol
q-Pochhammer symbol
Riemann zeta function
Sum of positive divisors function
Sine function
Tangent function
Theta functions
Totient function

Tools from calculus

Ratio test

Other

Solution manual to Rainville's "Special Functions"
"Special Functions" by Leon Hall