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

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=-35/8, b>=a

For fixed z and a=-35/8, b=-7/8

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

Input Form

Hypergeometric2F1[-(35/8), -(7/8), 5, z] == (65536 2^(1/4) (-4 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (6741504 - 89535600 z + 626815035 z^2 - 3807896400 z^3 - 35488550030 z^4 - 12412636964 z^5 + 1221422475 z^6 - 149230900 z^7 + 10381280 z^8) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (13483008 - 184127328 z + 1319399235 z^2 - 8068276755 z^3 + 93197351150 z^4 + 113498287802 z^5 + 624239343 z^6 - 75588695 z^7 + 5190640 z^8) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (6741504 - 89535600 z + 626815035 z^2 - 3807896400 z^3 - 35488550030 z^4 - 12412636964 z^5 + 1221422475 z^6 - 149230900 z^7 + 10381280 z^8) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 Sqrt[1 - z] (6741504 - 89535600 z + 626815035 z^2 - 3807896400 z^3 - 35488550030 z^4 - 12412636964 z^5 + 1221422475 z^6 - 149230900 z^7 + 10381280 z^8) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(5289993861487335 Pi (1 + Sqrt[1 - z])^(1/4) 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]