Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9f6)

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=-41/8, b>=a

For fixed z and a=-41/8, b=35/8

http://functions.wolfram.com/07.23.03.b9f6.01

Input Form

Hypergeometric2F1[-(41/8), 35/8, 3/2, -z] == (1/(7155837 Sqrt[z] (1 + z)^(7/8))) (4 (-4 Sqrt[z] (-412172 - 4861969 z - 13728519 z^2 - 3926592 z^3 + 30487808 z^4 + 39616512 z^5 + 14483456 z^6) Cos[(7 ArcTan[Sqrt[z]])/4] + (80155 + 6572334 z + 70864747 z^2 + 266361696 z^3 + 447632640 z^4 + 347017216 z^5 + 101384192 z^6) Sin[(7 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]