Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b8of)

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=-41/8, b>=a

For fixed z and a=-41/8, b=-37/8

http://functions.wolfram.com/07.23.03.b8of.01

Input Form

Hypergeometric2F1[-(41/8), -(37/8), 11/2, -z] == (1024 (Sqrt[z] (448 + 11256 z + 157913 z^2 + 1907128 z^3 + 139473100 z^4 - 944509800 z^5 + 1715971942 z^6 - 1097230456 z^7 + 246362284 z^8 - 15755600 z^9 + 126217 z^10) Cos[(7 ArcTan[Sqrt[z]])/4] - (256 + 6256 z + 85825 z^2 + 1028024 z^3 + 21342412 z^4 - 445201848 z^5 + 1461212662 z^6 - 1557251000 z^7 + 596776364 z^8 - 74772024 z^9 + 2061265 z^10) Sin[(7 ArcTan[Sqrt[z]])/4]))/ (103239068933 z^(9/2) (1 + z)^(7/8))

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]