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

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=23/4

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

Input Form

Hypergeometric2F1[-(17/4), 23/4, -(7/2), z] == (1/(9831360 Pi^(3/2))) (((1/(-1 + z)^5) (2 (-2457840 - 5179020 z - 14836283 z^2 - 64509522 z^3 - 739384107 z^4 + 6513808180 z^5 - 16112885760 z^6 + 18236596224 z^7 - 9923723264 z^8 + 2113929216 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^5) (2 (-2457840 - 5179020 z - 14836283 z^2 - 64509522 z^3 - 739384107 z^4 + 6513808180 z^5 - 16112885760 z^6 + 18236596224 z^7 - 9923723264 z^8 + 2113929216 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^4)) ((2457840 - 1228920 Sqrt[z] + 6407940 z - 3716020 z^(3/2) + 18552303 z^2 - 10867164 z^(5/2) + 75376686 z^3 - 42362628 z^(7/2) + 781746735 z^4 - 1760065780 z^(9/2) - 4753742400 z^5 + 7824168960 z^(11/2) + 8288716800 z^6 - 12230615040 z^(13/2) - 6005981184 z^7 + 8338276352 z^(15/2) + 1585446912 z^8 - 2113929216 z^(17/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^5)) ((2457840 + 1228920 Sqrt[z] + 6407940 z + 3716020 z^(3/2) + 18552303 z^2 + 10867164 z^(5/2) + 75376686 z^3 + 42362628 z^(7/2) + 781746735 z^4 + 1760065780 z^(9/2) - 4753742400 z^5 - 7824168960 z^(11/2) + 8288716800 z^6 + 12230615040 z^(13/2) - 6005981184 z^7 - 8338276352 z^(15/2) + 1585446912 z^8 + 2113929216 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]