Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b8og)

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=-41/8, b>=a

For fixed z and a=-41/8, b=-37/8

http://functions.wolfram.com/07.23.03.b8og.01

Input Form

Hypergeometric2F1[-(41/8), -(37/8), 23/4, z] == (16 2^(3/4) (4 (967846 - 23712227 z + 318509320 z^2 - 3513632924 z^3 + 2298014013940 z^4 + 10167222085030 z^5 + 12403253911848 z^6 + 5081398337556 z^7 + 652428420534 z^8 + 17843904069 z^9) + (1/Sqrt[1 - z]) (-3871384 + 96784600 z - 1320977811 z^2 + 14679936184 z^3 + 8772830745308 z^4 + 25654549618488 z^5 + 1486110804078 z^6 - 24259750471608 z^7 - 10660323546924 z^8 - 996472935312 z^9 - 10396085619 z^10)))/ (287548169425389 (1 + Sqrt[1 - z])^(3/4) 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]