Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aas4)

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=-17/4, b>=a

For fixed z and a=-17/4, b=15/4

http://functions.wolfram.com/07.23.03.aas4.01

Input Form

Hypergeometric2F1[-(17/4), 15/4, -(11/2), z] == (1/(13660416 Pi^(3/2))) (((1/(-1 + z)^5) (2 (-3415104 + 6752592 z - 970200 z^2 - 740355 z^3 - 943250 z^4 - 1891043 z^5 - 9791936 z^6 + 34803200 z^7 - 31621120 z^8 + 9175040 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^5) (2 (-3415104 + 6752592 z - 970200 z^2 - 740355 z^3 - 943250 z^4 - 1891043 z^5 - 9791936 z^6 + 34803200 z^7 - 31621120 z^8 + 9175040 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^4)) ((3415104 - 1707552 Sqrt[z] - 5045040 z + 1811040 z^(3/2) - 840840 z^2 + 1115730 z^(5/2) - 375375 z^3 + 691460 z^(7/2) + 251790 z^4 + 213290 z^(9/2) + 1677753 z^5 - 704704 z^(11/2) + 10496640 z^6 - 17323520 z^(13/2) - 17479680 z^7 + 24739840 z^(15/2) + 6881280 z^8 - 9175040 z^(17/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^5)) ((-3415104 - 1707552 Sqrt[z] + 5045040 z + 1811040 z^(3/2) + 840840 z^2 + 1115730 z^(5/2) + 375375 z^3 + 691460 z^(7/2) - 251790 z^4 + 213290 z^(9/2) - 1677753 z^5 - 704704 z^(11/2) - 10496640 z^6 - 17323520 z^(13/2) + 17479680 z^7 + 24739840 z^(15/2) - 6881280 z^8 - 9175040 z^(17/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)

Standard Form

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MathML 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]