Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7t9)

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=-23/4, b>=a

For fixed z and a=-23/4, b=21/4

http://functions.wolfram.com/07.23.03.a7t9.01

Input Form

Hypergeometric2F1[-(23/4), 21/4, 11/2, z] == (1/(1772646243225 Pi^(3/2) z^(9/2))) (32 (2 (56530320 + 131231100 z + 421184533 z^2 + 2087483013 z^3 + 27836841879 z^4 - 295859752925 z^5 + 916707453600 z^6 - 1385169106944 z^7 + 1131708153856 z^8 - 482504343552 z^9 + 84557168640 z^10) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (56530320 + 131231100 z + 421184533 z^2 + 2087483013 z^3 + 27836841879 z^4 - 295859752925 z^5 + 916707453600 z^6 - 1385169106944 z^7 + 1131708153856 z^8 - 482504343552 z^9 + 84557168640 z^10) EllipticE[(1/2) (1 + Sqrt[z])] - (56530320 + 28265160 Sqrt[z] + 131231100 z + 67970980 z^(3/2) + 421184533 z^2 + 217237944 z^(5/2) + 2087483013 z^3 + 1064788956 z^(7/2) + 27836841879 z^4 - 41378689880 z^(9/2) - 295859752925 z^5 + 164249384280 z^(11/2) + 916707453600 z^6 - 282956136960 z^(13/2) - 1385169106944 z^7 + 252221390848 z^(15/2) + 1131708153856 z^8 - 114680659968 z^(17/2) - 482504343552 z^9 + 21139292160 z^(19/2) + 84557168640 z^10) EllipticK[(1/2) (1 - Sqrt[z])] + (56530320 - 28265160 Sqrt[z] + 131231100 z - 67970980 z^(3/2) + 421184533 z^2 - 217237944 z^(5/2) + 2087483013 z^3 - 1064788956 z^(7/2) + 27836841879 z^4 + 41378689880 z^(9/2) - 295859752925 z^5 - 164249384280 z^(11/2) + 916707453600 z^6 + 282956136960 z^(13/2) - 1385169106944 z^7 - 252221390848 z^(15/2) + 1131708153856 z^8 + 114680659968 z^(17/2) - 482504343552 z^9 - 21139292160 z^(19/2) + 84557168640 z^10) 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]