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

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=7/4, b>=a

For fixed z and a=7/4, b=17/4

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

Input Form

Hypergeometric2F1[7/4, 17/4, -(7/2), -z] == (1/(80 Sqrt[2] Sqrt[-1 + Sqrt[1 + z]])) (Sqrt[z] ((2 (20 + 230 z + 1306 z^2 + 5385 z^3 + 147724 z^4 - 96724 z^5 - 850 z^6 - 51 z^7))/(1 + z)^(19/2) + (40 + 440 z + 2397 z^2 + 9624 z^3 - 184082 z^4 + 50796 z^5 + 3349 z^6 + 204 z^7)/(1 + z)^9))

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]