kummers formulas

Input interpretation

Kummer's formulas

Definition

Kummer's first formula is _2 F_1(1/2 + m - k, - n;2m + 1;1) = (Γ(2m + 1) Γ(m + 1/2 + k + n))/(Γ(m + 1/2 + k) Γ(2m + 1 + n)), where _2 F_1(a, b;c;z) is the hypergeometric function with m!=-1/2, -1, -3/2, ..., and Γ(z) is the gamma function.
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Related terms

confluent hypergeometric function of the first kind | hypergeometric function
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