Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b89y)

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=41/8

http://functions.wolfram.com/07.23.03.b89y.01

Input Form

Hypergeometric2F1[-(43/8), 41/8, 21/4, z] == (16 2^(1/4) (-4 (191178 + 507357 z + 1816191 z^2 + 10534398 z^3 - 452063199 z^4 + 1885808507 z^5 - 3378012352 z^6 + 3111423744 z^7 - 1455587328 z^8 + 275185664 z^9) + (1/Sqrt[1 - z]) (764712 + 1647072 z + 6154461 z^2 + 38203737 z^3 + 3929252607 z^4 - 25019220941 z^5 + 64061149328 z^6 - 86537541376 z^7 + 65433059328 z^8 - 26316439552 z^9 + 4402970624 z^10)))/ (92154224085 (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]