Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ce0f)

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=45/8, b>=a

For fixed z and a=45/8, b=47/8

http://functions.wolfram.com/07.23.03.ce0f.01

Input Form

Hypergeometric2F1[45/8, 47/8, 2, z] == (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-1 + z) (723695 + 68181412 z + 273739386 z^2 + 189230692 z^3 + 19610255 z^4) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 36 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-3618475 - 24588948 z - 28124994 z^2 - 5095188 z^3 + 151445 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (26197759 + 190676708 z + 257247834 z^2 + 74531492 z^3 + 2831647 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-1 + z) (723695 + 68181412 z + 273739386 z^2 + 189230692 z^3 + 19610255 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (1044291885 Pi (-1 + z)^10 z)

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]