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

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=43/8, b>=a

For fixed z and a=43/8, b=45/8

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

Input Form

Hypergeometric2F1[43/8, 45/8, -(9/2), -z] == (1/(7691264 (1 + z)^(31/2))) ((-Sqrt[1 + z]) (-7691264 - 169207808 z - 1940863860 z^2 - 16459657977 z^3 - 134295666015 z^4 - 1954286932269 z^5 + 14530669687901 z^6 - 20218023810955 z^7 + 8169445755459 z^8 - 889560536207 z^9 + 14473166323 z^10) Cosh[(3 ArcSinh[Sqrt[z]])/4] + Sqrt[z] (-5768448 - 127747088 z - 1473629229 z^2 - 12545833608 z^3 - 102397312780 z^4 - 4666507383576 z^5 + 21510586810386 z^6 - 24838156671416 z^7 + 9017686555572 z^8 - 919585254168 z^9 + 14473166323 z^10) Sinh[(3 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]