Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ak0s)

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=19/4

http://functions.wolfram.com/07.23.03.ak0s.01

Input Form

Hypergeometric2F1[5/4, 19/4, -(7/2), -z] == (1/(112 Sqrt[2] Sqrt[-1 + Sqrt[1 + z]])) (Sqrt[z] ((56 + 592 z + 3045 z^2 + 11176 z^3 - 156178 z^4 + 5700 z^5 + 893 z^6 + 76 z^7)/(1 + z)^9 + (2 (28 + 310 z + 1667 z^2 + 6314 z^3 + 133826 z^4 - 46322 z^5 - 6365 z^6 - 950 z^7 - 76 z^8))/(1 + z)^(19/2)))

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]