Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ba8l)

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=-39/8, b>=a

For fixed z and a=-39/8, b=13/8

http://functions.wolfram.com/07.23.03.ba8l.01

Input Form

Hypergeometric2F1[-(39/8), 13/8, 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-303726592 + 2430999168 z - 8124120927 z^2 + 13613491528 z^3 - 6590425842 z^4 + 12570339276 z^5 - 11041919559 z^6 + 5594312196 z^7 - 1571733504 z^8 + 190688256 z^9) EllipticE[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-303726592 + 2430999168 z - 8124120927 z^2 + 13613491528 z^3 - 6590425842 z^4 + 12570339276 z^5 - 11041919559 z^6 + 5594312196 z^7 - 1571733504 z^8 + 190688256 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (-303726592 + 2430999168 z - 8124120927 z^2 + 13613491528 z^3 - 6590425842 z^4 + 12570339276 z^5 - 11041919559 z^6 + 5594312196 z^7 - 1571733504 z^8 + 190688256 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (-303726592 + 2544896640 z - 9004601775 z^2 + 16427309665 z^3 - 10984043070 z^4 - 46743493302 z^5 + 69370537005 z^6 - 54261649035 z^7 + 25308629280 z^8 - 6652419840 z^9 + 762753024 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (15926055124334355 Pi (1 + Sqrt[1 - z])^(1/4) z^5)

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]