Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ak26)

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=5/4, b>=a

For fixed z and a=5/4, b=5

http://functions.wolfram.com/07.23.03.ak26.01

Input Form

Hypergeometric2F1[5/4, 5, -(13/4), z] == (1/(3328 (-1 + z)^10)) (4 (832 - 9920 z + 58240 z^2 - 248960 z^3 + 1864000 z^4 - 1030181 z^5 - 748510 z^6 + 133364 z^7 - 20482 z^8 + 1617 z^9) - 231 Sqrt[1 - z] z^(17/4) (-15225 - 2900 z + 522 z^2 - 84 z^3 + 7 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]