Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7c6)

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=47/8

http://functions.wolfram.com/07.23.03.b7c6.01

Input Form

Hypergeometric2F1[-(45/8), 47/8, 9/2, z] == (1/(313624632685 z^(7/2))) (128 ((1 + Sqrt[z])^(17/4) (343360 - 1459280 Sqrt[z] + 6807112 z - 20630571 z^(3/2) + 74878232 z^2 - 208677040 z^(5/2) + 1031110080 z^3 - 2070964480 z^(7/2) - 6665052160 z^4 + 28622929920 z^(9/2) - 25997803520 z^5 - 23390781440 z^(11/2) + 59440103424 z^6 - 40304115712 z^(13/2) + 9483321344 z^7) - (1 - Sqrt[z])^(17/4) (343360 + 1459280 Sqrt[z] + 6807112 z + 20630571 z^(3/2) + 74878232 z^2 + 208677040 z^(5/2) + 1031110080 z^3 + 2070964480 z^(7/2) - 6665052160 z^4 - 28622929920 z^(9/2) - 25997803520 z^5 + 23390781440 z^(11/2) + 59440103424 z^6 + 40304115712 z^(13/2) + 9483321344 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]