Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7gj)

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=-43/8, b>=a

For fixed z and a=-43/8, b=-31/8

http://functions.wolfram.com/07.23.03.b7gj.01

Input Form

Hypergeometric2F1[-(43/8), -(31/8), 21/4, z] == (16 2^(1/4) (95976 - 2303424 z + 31396149 z^2 - 390866259 z^3 + 49247471721 z^4 + 223659333601 z^5 + 252847299199 z^6 + 84128758791 z^7 + 6538942011 z^8 - 756245 z^9 + (1/Sqrt[1 - z]) (4 (-23994 + 587853 z - 8133966 z^2 + 101570601 z^3 + 5607789369 z^4 + 11404650895 z^5 - 4160310715 z^6 - 10360887229 z^7 - 2507349579 z^8 - 78649480 z^9 + 756245 z^10))))/(1149924448365 (1 + Sqrt[1 - z])^(1/4) z^4)

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]