Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b771)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-45/8, b>=a

For fixed z and a=-45/8, b=39/8

http://functions.wolfram.com/07.23.03.b771.01

Input Form

Hypergeometric2F1[-(45/8), 39/8, 11/2, z] == (1/(2388372202755 z^(9/2))) (512 ((1 + Sqrt[z])^(25/4) (9614080 - 60088000 Sqrt[z] + 228248560 z - 664187000 z^(3/2) + 1647659099 z^2 - 3653028500 z^(5/2) + 7532202480 z^3 - 14730144000 z^(7/2) + 28871082240 z^4 - 55366108160 z^(9/2) + 86198435840 z^5 - 92527001600 z^(11/2) + 62072750080 z^6 - 23284940800 z^(13/2) + 3725590528 z^7) - (1 - Sqrt[z])^(25/4) (9614080 + 60088000 Sqrt[z] + 228248560 z + 664187000 z^(3/2) + 1647659099 z^2 + 3653028500 z^(5/2) + 7532202480 z^3 + 14730144000 z^(7/2) + 28871082240 z^4 + 55366108160 z^(9/2) + 86198435840 z^5 + 92527001600 z^(11/2) + 62072750080 z^6 + 23284940800 z^(13/2) + 3725590528 z^7)))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]