Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b8wj)

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=-5/8

http://functions.wolfram.com/07.23.03.b8wj.01

Input Form

Hypergeometric2F1[-(41/8), -(5/8), 3/2, -z] == (1/(878787 Sqrt[z] (1 + z)^(7/8))) (4 (Sqrt[z] (286783 - 1460284 z + 303282 z^2 + 105060 z^3 + 46663 z^4 + 13584 z^5 + 1792 z^6) Cos[(7 ArcTan[Sqrt[z]])/4] - (38335 - 894804 z + 1221538 z^2 + 251076 z^3 + 99351 z^4 + 25928 z^5 + 3136 z^6) Sin[(7 ArcTan[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]