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

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=5

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

Input Form

Hypergeometric2F1[-(15/4), 5, -(17/4), z] == (1/(2715648 (-1 + z)^6)) (4 (-1 + z) (-678912 + 399360 z + 583680 z^2 + 1054720 z^3 + 2959360 z^4 + 36345856 z^5 - 151570695 z^6 + 208397871 z^7 - 125073333 z^8 + 28164213 z^9) - 231 Sqrt[1 - z] z^(21/4) (295075 - 897028 z + 1067154 z^2 - 582084 z^3 + 121923 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]