Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9215)

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=-11/4

http://functions.wolfram.com/07.23.03.9215.01

Input Form

Hypergeometric2F1[-(23/4), -(11/4), 11/2, z] == (32 (-2 (11306064 - 238638708 z + 2746330433 z^2 - 26383339675 z^3 + 408411540845 z^4 + 3028808709193 z^5 + 3646247754259 z^6 + 967359821791 z^7 + 13824309135 z^8 - 630549465 z^9 + 21534240 z^10) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (11306064 - 238638708 z + 2746330433 z^2 - 26383339675 z^3 + 408411540845 z^4 + 3028808709193 z^5 + 3646247754259 z^6 + 967359821791 z^7 + 13824309135 z^8 - 630549465 z^9 + 21534240 z^10) EllipticE[(1/2) (1 + Sqrt[z])] + (11306064 + 5653032 Sqrt[z] - 238638708 z - 118848268 z^(3/2) + 2746330433 z^2 + 1363457480 z^(5/2) - 26383339675 z^3 - 13082058220 z^(7/2) + 408411540845 z^4 + 933369955600 z^(9/2) + 3028808709193 z^5 + 3538982527684 z^(11/2) + 3646247754259 z^6 + 3001326466024 z^(13/2) + 967359821791 z^7 + 578482364460 z^(15/2) + 13824309135 z^8 - 156123240 z^(17/2) - 630549465 z^9 + 5383560 z^(19/2) + 21534240 z^10) EllipticK[(1/2) (1 - Sqrt[z])] - (11306064 - 5653032 Sqrt[z] - 238638708 z + 118848268 z^(3/2) + 2746330433 z^2 - 1363457480 z^(5/2) - 26383339675 z^3 + 13082058220 z^(7/2) + 408411540845 z^4 - 933369955600 z^(9/2) + 3028808709193 z^5 - 3538982527684 z^(11/2) + 3646247754259 z^6 - 3001326466024 z^(13/2) + 967359821791 z^7 - 578482364460 z^(15/2) + 13824309135 z^8 + 156123240 z^(17/2) - 630549465 z^9 - 5383560 z^(19/2) + 21534240 z^10) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)/ (23366700478875 Pi^(3/2) z^(9/2))

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]