Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c3o0)

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=11/8, b>=a

For fixed z and a=11/8, b=37/8

http://functions.wolfram.com/07.23.03.c3o0.01

Input Form

Hypergeometric2F1[11/8, 37/8, -(9/2), z] == (1/(1870848 (1 - z)^(21/2))) (4 Sqrt[1 - z] (467712 - 5469632 z + 30381821 z^2 - 109966695 z^3 + 319451965 z^4 - 1249277428 z^5 - 1146176733 z^6 + 73020469 z^7 - 8679349 z^8 + 603198 z^9) Cos[(3 ArcSin[Sqrt[z]])/4] + Sqrt[z] (1403136 - 16613520 z + 93410537 z^2 - 341787765 z^3 + 999155850 z^4 - 7461408802 z^5 - 4726558995 z^6 + 309138975 z^7 - 35923792 z^8 + 2412792 z^9) Sin[(3 ArcSin[Sqrt[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]