Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9of)

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=-39/8, b>=a

For fixed z and a=-39/8, b=-35/8

http://functions.wolfram.com/07.23.03.b9of.01

Input Form

Hypergeometric2F1[-(39/8), -(35/8), 11/2, -z] == -((1024 (Sqrt[z] (-448 - 10552 z - 138201 z^2 - 1553279 z^3 - 547230541 z^4 + 2276850069 z^5 - 2469131819 z^6 + 826300867 z^7 - 73097007 z^8 + 770847 z^9) Cos[ArcTan[Sqrt[z]]/4] + (1792 + 42768 z + 565847 z^2 + 6382481 z^3 + 119138019 z^4 - 1361296651 z^5 + 2750459621 z^6 - 1658750541 z^7 + 297139873 z^8 - 11028873 z^9) Sin[ArcTan[Sqrt[z]]/4]))/(530350628005 z^(9/2) (1 + z)^(1/8)))

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]