Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6ik)

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=-3/8

http://functions.wolfram.com/07.23.03.b6ik.01

Input Form

Hypergeometric2F1[-(45/8), -(3/8), 5/2, z] == (1/(35689885 z^(3/2))) (16 ((-Sqrt[z]) (41847 - 3345666 z - 7327278 z^2 + 1868736 z^3 - 851121 z^4 + 302778 z^5 - 68016 z^6 + 7072 z^7) Cos[(3 ArcSin[Sqrt[z]])/4] - (1/Sqrt[1 - z]) (2 (-27898 + 767195 z + 2577863 z^2 - 4085858 z^3 + 1130212 z^4 - 497225 z^5 + 167951 z^6 - 35776 z^7 + 3536 z^8) 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]