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Special functions

Binomial function
Dedekind eta function
Jacobi elliptic functions
Gamma function
Generalized hypergeometric function ${}_pF_q$
Pochhammer symbol
q-Pochhammer symbol
Riemann zeta function
Theta functions
Trigonometric functions

Tools from calculus

Ratio test

Other

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