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

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=-29/8, b>=a

For fixed z and a=-29/8, b=15/8

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

Input Form

Hypergeometric2F1[-(29/8), 15/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (12353536 - 82276480 z + 218733515 z^2 - 264375020 z^3 + 33647250 z^4 - 71115420 z^5 + 53449275 z^6 - 19645200 z^7 + 2937600 z^8) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (12353536 - 82276480 z + 218733515 z^2 - 264375020 z^3 + 33647250 z^4 - 71115420 z^5 + 53449275 z^6 - 19645200 z^7 + 2937600 z^8) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (12353536 - 82276480 z + 218733515 z^2 - 264375020 z^3 + 33647250 z^4 - 71115420 z^5 + 53449275 z^6 - 19645200 z^7 + 2937600 z^8) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (12353536 - 86909056 z + 248320475 z^2 - 338636480 z^3 + 114400650 z^4 + 251898180 z^5 - 379167405 z^6 + 250200900 z^7 - 84211200 z^8 + 11750400 z^9) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (83315796229575 Pi (1 + Sqrt[1 - z])^(1/4) (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]