Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9j1)

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=43/8

http://functions.wolfram.com/07.23.03.b9j1.01

Input Form

Hypergeometric2F1[-(41/8), 43/8, -(9/2), -z] == (1/(3677184 (1 + z)^(31/8))) ((3677184 - 13891584 z + 35660340 z^2 - 88647825 z^3 + 268865751 z^4 - 1781653104 z^5 - 4393276160 z^6 + 2825338880 z^7 + 9428729856 z^8 + 4402970624 z^9) Cos[(7 ArcTan[Sqrt[z]])/4] - Sqrt[z] (-6435072 + 19886160 z - 48457353 z^2 + 120900591 z^3 - 385090860 z^4 + 4926398464 z^5 + 19599111168 z^6 + 21797601280 z^7 + 7705198592 z^8) Sin[(7 ArcTan[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]