Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6qo)

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=-45/8, b>=a

For fixed z and a=-45/8, b=13/8

http://functions.wolfram.com/07.23.03.b6qo.01

Input Form

Hypergeometric2F1[-(45/8), 13/8, 11/2, z] == (1/(77044264605 z^(9/2))) (1024 (4 Sqrt[z] (-360528 + 2972210 z - 10052937 z^2 + 15547770 z^3 + 26943902 z^4 - 55572462 z^5 + 59508015 z^6 - 39860518 z^7 + 16764516 z^8 - 4072656 z^9 + 437920 z^10) Cos[(3 ArcSin[Sqrt[z]])/4] + (1/Sqrt[1 - z]) ((1922816 - 17494192 z + 67091471 z^2 - 128222427 z^3 + 25912950 z^4 + 196921722 z^5 - 324978293 z^6 + 310320577 z^7 - 191044256 z^8 + 74984416 z^9 - 17166464 z^10 + 1751680 z^11) Sin[(3 ArcSin[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]