Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bq3k)

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=-13/8, b>=a

For fixed z and a=-13/8, b=5/8

http://functions.wolfram.com/07.23.03.bq3k.01

Input Form

Hypergeometric2F1[-(13/8), 5/8, 11/2, -z] == (1/(191329985 z^(9/2) Sqrt[1 + z])) (1024 (Sqrt[z] Sqrt[1 + z] (12480 + 83720 z + 243607 z^2 + 412841 z^3 + 747937 z^4 + 116219 z^5 + 14260 z^6) Cosh[(3 ArcSinh[Sqrt[z]])/4] - (16640 + 125840 z + 419601 z^2 + 824460 z^3 + 1209234 z^4 + 804264 z^5 + 123349 z^6 + 14260 z^7) 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]