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

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-15/4, b>=a

For fixed z and a=-15/4, b=19/4

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

Input Form

Hypergeometric2F1[-(15/4), 19/4, 5/2, -z] == (1/(1547 z^(3/2) Sqrt[-1 + Sqrt[1 + z]])) (2 Sqrt[2] (-2 (-1 + 34 z + 524 z^2 + 1736 z^3 + 2080 z^4 + 832 z^5) + (-2 + 67 z + 1469 z^2 + 6888 z^3 + 12976 z^4 + 10816 z^5 + 3328 z^6)/ Sqrt[1 + z]))

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]