Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c9za)

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=25/8, b>=a

For fixed z and a=25/8, b=47/8

http://functions.wolfram.com/07.23.03.c9za.01

Input Form

Hypergeometric2F1[25/8, 47/8, -(5/2), -z] == (1/(45632 (1 + z)^(23/2))) ((-Sqrt[1 + z]) (-45632 - 838488 z - 9389497 z^2 - 146325425 z^3 + 794984298 z^4 - 564154842 z^5 + 39172011 z^6 + 2063379 z^7 + 90132 z^8) Cosh[ArcSinh[Sqrt[z]]/4] + Sqrt[z] (-11408 - 213187 z - 2411366 z^2 - 1377408365 z^3 + 3314558160 z^4 - 1408335693 z^5 + 40192434 z^6 + 2108445 z^7 + 90132 z^8) 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]