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

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=5

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

Input Form

Hypergeometric2F1[-(7/4), 5, 23/4, z] == (1/(40894464 z^(19/4))) (19 (4 z^(3/4) (8085 + 5236 z + 5957 z^2 + 10248 z^3 + 572935 z^4 - 1082620 z^5 + 504735 z^6) - 231 (1 - z)^(5/2) (105 + 308 z + 630 z^2 + 1140 z^3 + 2185 z^4) Beta[z, 3/4, 1/2]))

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]