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

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=-9/4, b>=a

For fixed z and a=-9/4, b=17/4

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

Input Form

Hypergeometric2F1[-(9/4), 17/4, 6, z] == (1/(131224275 Pi Sqrt[1 + Sqrt[z]] z^5)) (16384 ((2048 + 2048 Sqrt[z] - 2400 z - 2400 z^(3/2) - 1037 z^2 - 1037 z^(5/2) - 1070 z^3 - 1070 z^(7/2) - 2205 z^4 - 2205 z^(9/2) + 33544 z^5 + 33544 z^(11/2) - 42000 z^6 - 42000 z^(13/2) + 14784 z^7 + 14784 z^(15/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (2048 - 2912 z - 581 z^2 - 720 z^3 - 1825 z^4 + 18214 z^5 - 21616 z^6 + 7392 z^7) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))

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]