Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c7lx)

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=19/8, b>=a

For fixed z and a=19/8, b=45/8

http://functions.wolfram.com/07.23.03.c7lx.01

Input Form

Hypergeometric2F1[19/8, 45/8, -(7/2), z] == -((1/(1922816 (1 - z)^(23/2))) (Sqrt[1 - z] (-1922816 + 29031088 z - 227165903 z^2 + 1384722595 z^3 - 12322922150 z^4 - 40212231602 z^5 - 13139428523 z^6 + 519588055 z^7 - 44502608 z^8 + 2412792 z^9) Cos[(3 ArcSin[Sqrt[z]])/4] + 4 Sqrt[z] (-360528 + 5495906 z - 43354565 z^2 + 265374360 z^3 - 5943585313 z^4 - 12397150640 z^5 - 3348452631 z^6 + 135384440 z^7 - 11427251 z^8 + 603198 z^9) 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]