Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6io)

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=-3/8

http://functions.wolfram.com/07.23.03.b6io.01

Input Form

Hypergeometric2F1[-(45/8), -(3/8), 9/2, z] == (1/(265374689195 z^(7/2))) (256 ((-Sqrt[z]) (772560 - 10870563 z + 84308829 z^2 - 1788498228 z^3 - 2277748374 z^4 + 351341445 z^5 - 108466551 z^6 + 27939618 z^7 - 4757136 z^8 + 387872 z^9) Cos[(3 ArcSin[Sqrt[z]])/4] - (1/Sqrt[1 - z]) (2 (-515040 + 7686972 z - 62378855 z^2 + 549028348 z^3 + 573791977 z^4 - 1220715892 z^5 + 201182219 z^6 - 60932980 z^7 + 15134851 z^8 - 2475536 z^9 + 193936 z^10) 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]