Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aep2)

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=23/4

http://functions.wolfram.com/07.23.03.aep2.01

Input Form

Hypergeometric2F1[-(9/4), 23/4, -(7/2), z] == (1/(1966272 Pi^(3/2))) (((1/(-1 + z)^7) (2 (-491568 + 1562484 z - 498883 z^2 - 809039 z^3 - 4516281 z^4 + 21911879 z^5 - 34953152 z^6 + 27723264 z^7 - 11173888 z^8 + 1835008 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^7) (2 (-491568 + 1562484 z - 498883 z^2 - 809039 z^3 - 4516281 z^4 + 21911879 z^5 - 34953152 z^6 + 27723264 z^7 - 11173888 z^8 + 1835008 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((491568 - 245784 Sqrt[z] - 1316700 z + 555940 z^(3/2) - 57057 z^2 + 251636 z^(5/2) + 557403 z^3 - 158004 z^(7/2) + 4674285 z^4 - 8501900 z^(9/2) - 13409979 z^5 + 20578112 z^(11/2) + 14375040 z^6 - 20590080 z^(13/2) - 7133184 z^7 + 9797632 z^(15/2) + 1376256 z^8 - 1835008 z^(17/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((491568 + 245784 Sqrt[z] - 1316700 z - 555940 z^(3/2) - 57057 z^2 - 251636 z^(5/2) + 557403 z^3 + 158004 z^(7/2) + 4674285 z^4 + 8501900 z^(9/2) - 13409979 z^5 - 20578112 z^(11/2) + 14375040 z^6 + 20590080 z^(13/2) - 7133184 z^7 - 9797632 z^(15/2) + 1376256 z^8 + 1835008 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]