Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.amg5)

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=21/4

http://functions.wolfram.com/07.23.03.amg5.01

Input Form

Hypergeometric2F1[13/4, 21/4, -(3/2), z] == (1/(13260 Pi^(3/2))) (((1/(-1 + z)^10) (4 Sqrt[z] (3315 - 69615 z - 26188956 z^2 - 65254710 z^3 - 25528221 z^4 - 416955 z^5 + 14630 z^6) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^10) (4 Sqrt[z] (3315 - 69615 z - 26188956 z^2 - 65254710 z^3 - 25528221 z^4 - 416955 z^5 + 14630 z^6) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^10 (1 + Sqrt[z])^9)) ((13260 - 19890 Sqrt[z] - 268515 z + 407745 z^(3/2) + 5807880 z^2 + 46570032 z^(5/2) + 32095374 z^3 + 98414046 z^(7/2) + 20289552 z^4 + 30766890 z^(9/2) + 811965 z^5 + 21945 z^(11/2) - 29260 z^6) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^10)) ((-13260 - 19890 Sqrt[z] + 268515 z + 407745 z^(3/2) - 5807880 z^2 + 46570032 z^(5/2) - 32095374 z^3 + 98414046 z^(7/2) - 20289552 z^4 + 30766890 z^(9/2) - 811965 z^5 + 21945 z^(11/2) + 29260 z^6) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^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]