Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.abd8)

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=3/4

http://functions.wolfram.com/07.23.03.abd8.01

Input Form

Hypergeometric2F1[-(15/4), 3/4, 9/2, -z] == (1/(96135 z^(7/2) Sqrt[-1 + Sqrt[1 + z]])) (8 Sqrt[2] (-4 (30 + 243 z + 901 z^2 + 2390 z^3 + 722 z^4 + 361 z^5 + 107 z^6 + 14 z^7) + (120 + 1032 z + 4075 z^2 + 11248 z^3 + 13282 z^4 + 7892 z^5 + 3523 z^6 + 940 z^7 + 112 z^8)/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]