Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.amf4)

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=13/4, b>=a

For fixed z and a=13/4, b=5

http://functions.wolfram.com/07.23.03.amf4.01

Input Form

Hypergeometric2F1[13/4, 5, -(17/4), z] == (1/(1632 (-1 + z)^13)) (4 (-1 + z) (408 - 6456 z + 51768 z^2 - 299480 z^3 + 1682120 z^4 - 26032296 z^5 - 53471633 z^6 - 17527015 z^7 - 509355 z^8 + 10395 z^9) - 231 Sqrt[1 - z] z^(21/4) (-295075 - 424908 z - 109890 z^2 - 2220 z^3 + 45 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]