Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bd0b)

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=-35/8, b>=a

For fixed z and a=-35/8, b=25/8

http://functions.wolfram.com/07.23.03.bd0b.01

Input Form

Hypergeometric2F1[-(35/8), 25/8, -(9/2), -z] == (1/(156672 (1 + z)^(21/8))) (-2 (-78336 + 93568 z - 89726 z^2 + 73185 z^3 - 26520 z^4 - 231744 z^5 + 1272832 z^6 + 1171456 z^7) Cos[(5 ArcTan[Sqrt[z]])/4] + Sqrt[z] (195840 - 197200 z + 181373 z^2 - 140709 z^3 + 31008 z^4 + 3731200 z^5 + 2928640 z^6) Sin[(5 ArcTan[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]