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

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=-7/4, b>=a

For fixed z and a=-7/4, b=23/4

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

Input Form

Hypergeometric2F1[-(7/4), 23/4, -(5/2), -z] == (1/(760 Sqrt[2] Sqrt[-1 + Sqrt[1 + z]])) (Sqrt[z] (-((-380 - 703 z + 969 z^2 + 14407 z^3 + 30467 z^4 + 29016 z^5 + 13488 z^6 + 2496 z^7)/(1 + z)^6) + (1/(1 + z)^(13/2)) (380 + 893 z - 665 z^2 + 21095 z^3 + 71633 z^4 + 102928 z^5 + 77952 z^6 + 30720 z^7 + 4992 z^8)))

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]