Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c2i5)

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=9/8, b>=a

For fixed z and a=9/8, b=31/8

http://functions.wolfram.com/07.23.03.c2i5.01

Input Form

Hypergeometric2F1[9/8, 31/8, -(11/2), -z] == (1/(7254016 (1 + z)^(21/2))) ((-Sqrt[1 + z]) (-7254016 - 78516480 z - 392917280 z^2 - 1218409061 z^3 - 2693760897 z^4 - 4927705334 z^5 - 12323080530 z^6 + 3204852495 z^7 + 309765443 z^8 + 20700316 z^9) Cosh[ArcSinh[Sqrt[z]]/4] + Sqrt[z] (-1813504 - 20195840 z - 104122564 z^2 - 332832287 z^3 - 757007027 z^4 - 1408570186 z^5 - 46273599690 z^6 + 3357147677 z^7 + 320115601 z^8 + 20700316 z^9) Sinh[ArcSinh[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]