Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bc96)

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=41/8

http://functions.wolfram.com/07.23.03.bc96.01

Input Form

Hypergeometric2F1[-(37/8), 41/8, 4, z] == (2048 2^(1/4) (2 Sqrt[1 - z] (-12498304 - 108090801 z - 1108736265 z^2 + 89990135290 z^3 - 430088862480 z^4 + 763517883744 z^5 - 590422043904 z^6 + 168234232320 z^7) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-12498304 - 108090801 z - 1108736265 z^2 + 89990135290 z^3 - 430088862480 z^4 + 763517883744 z^5 - 590422043904 z^6 + 168234232320 z^7) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (-12498304 - 100279361 z - 1039897950 z^2 + 25840148935 z^3 - 98859031480 z^4 + 152873067024 z^5 - 106748625984 z^6 + 28039038720 z^7) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-12498304 - 108090801 z - 1108736265 z^2 + 89990135290 z^3 - 430088862480 z^4 + 763517883744 z^5 - 590422043904 z^6 + 168234232320 z^7) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (66411141922125 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^3)

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]