Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6m7)

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=5/8

http://functions.wolfram.com/07.23.03.b6m7.01

Input Form

Hypergeometric2F1[-(45/8), 5/8, 11/2, z] == (1/(2388372202755 z^(9/2))) (1024 (Sqrt[z] (7210560 - 80303320 z + 418428153 z^2 - 1407189069 z^3 + 6714909938 z^4 - 3228636546 z^5 + 1987847565 z^6 - 935422489 z^7 + 303241752 z^8 - 59926224 z^9 + 5430208 z^10) Cos[(3 ArcSin[Sqrt[z]])/4] + (1/Sqrt[1 - z]) ((-9614080 + 115283120 z - 649039459 z^2 + 2349387150 z^3 - 7429126881 z^4 + 8128893036 z^5 - 4122392741 z^6 + 2421186862 z^7 - 1079891975 z^8 + 332526088 z^9 - 62641328 z^10 + 5430208 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]