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

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=1/4, b>=a

For fixed z and a=1/4, b=6

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

Input Form

Hypergeometric2F1[1/4, 6, -(13/4), z] == (1/(79872 (-1 + z)^10)) (4 (19968 - 208896 z + 1008640 z^2 - 3076096 z^3 + 9481728 z^4 - 12525527 z^5 + 8396759 z^6 - 4320414 z^7 + 1512742 z^8 - 319627 z^9 + 30723 z^10) - 231 Sqrt[1 - z] z^(17/4) (-37555 + 26825 z - 15022 z^2 + 5698 z^3 - 1295 z^4 + 133 z^5) 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]