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

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=-7/8, b>=a

For fixed z and a=-7/8, b=39/8

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

Input Form

Hypergeometric2F1[-(7/8), 39/8, -(11/2), z] == -((1/(96374784 (1 - z)^(19/2))) (Sqrt[1 - z] (-96374784 + 795639552 z - 2814467680 z^2 + 5424876899 z^3 - 5739514530 z^4 + 2088583770 z^5 + 3341734032 z^6 - 4389262085 z^7 + 2522230282 z^8 - 748782320 z^9 + 93290912 z^10) Cos[ArcSin[Sqrt[z]]/4] + 2 Sqrt[z] (-12046848 + 103219584 z - 381288158 z^2 + 775773233 z^3 - 889693521 z^4 + 417716754 z^5 + 2632120504 z^6 - 2781305059 z^7 + 1442480039 z^8 - 397713888 z^9 + 46645456 z^10) Sin[ArcSin[Sqrt[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]