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

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=3/4, b>=a

For fixed z and a=3/4, b=23/4

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

Input Form

Hypergeometric2F1[3/4, 23/4, -(7/2), z] == (1/(9831360 Pi^(3/2))) (((1/(-1 + z)^10) (2 (2457840 - 27299580 z + 144750683 z^2 - 519834623 z^3 + 2037716142 z^4 + 657755670 z^5 - 242561865 z^6 + 74247381 z^7 - 14660256 z^8 + 1357824 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^10) (2 (2457840 - 27299580 z + 144750683 z^2 - 519834623 z^3 + 2037716142 z^4 + 657755670 z^5 - 242561865 z^6 + 74247381 z^7 - 14660256 z^8 + 1357824 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) - (1/((-1 + Sqrt[z])^10 (1 + Sqrt[z])^9)) ((2457840 - 1228920 Sqrt[z] - 26070660 z + 12523280 z^(3/2) + 132227403 z^2 - 60938339 z^(5/2) - 458896284 z^3 + 204474732 z^(7/2) + 1833241410 z^4 + 517730070 z^(9/2) + 140025600 z^5 - 195969540 z^(11/2) - 46592325 z^6 + 64175085 z^(13/2) + 10072296 z^7 - 13641888 z^(15/2) - 1018368 z^8 + 1357824 z^(17/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^10)) ((2457840 + 1228920 Sqrt[z] - 26070660 z - 12523280 z^(3/2) + 132227403 z^2 + 60938339 z^(5/2) - 458896284 z^3 - 204474732 z^(7/2) + 1833241410 z^4 - 517730070 z^(9/2) + 140025600 z^5 + 195969540 z^(11/2) - 46592325 z^6 - 64175085 z^(13/2) + 10072296 z^7 + 13641888 z^(15/2) - 1018368 z^8 - 1357824 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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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]