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

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=-37/8, b>=a

For fixed z and a=-37/8, b=-7/8

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

Input Form

Hypergeometric2F1[-(37/8), -(7/8), 6, z] == (524288 2^(1/4) (-2 Sqrt[1 - z] (-35160064 + 477819776 z - 3226042099 z^2 + 15442923951 z^3 - 73585522374 z^4 - 374205559482 z^5 - 75372170447 z^6 + 8457271603 z^7 - 970210472 z^8 + 61928328 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-35160064 + 477819776 z - 3226042099 z^2 + 15442923951 z^3 - 73585522374 z^4 - 374205559482 z^5 - 75372170447 z^6 + 8457271603 z^7 - 970210472 z^8 + 61928328 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-35160064 + 499794816 z - 3521074179 z^2 + 17411895046 z^3 - 82928492829 z^4 + 1048658977248 z^5 + 1030431076243 z^6 + 1456321038 z^7 - 164773587 z^8 + 10321388 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (-35160064 + 477819776 z - 3226042099 z^2 + 15442923951 z^3 - 73585522374 z^4 - 374205559482 z^5 - 75372170447 z^6 + 8457271603 z^7 - 970210472 z^8 + 61928328 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (361317083787554895 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] 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]