Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9599)

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=5/4

http://functions.wolfram.com/07.23.03.9599.01

Input Form

Hypergeometric2F1[-(23/4), 5/4, 3, -z] == (64 Sqrt[2] (Sqrt[1 + z] (672980 + 3533145 z + 15976539 z^2 + 29879179 z^3 + 31684341 z^4 + 19725696 z^5 + 6748160 z^6 + 983040 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (672980 + 4206125 z + 19509684 z^2 + 45855718 z^3 + 61563520 z^4 + 51410037 z^5 + 26473856 z^6 + 7731200 z^7 + 983040 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 4 (168245 + 1009470 z + 1344276 z^2 + 2294998 z^3 + 2277423 z^4 + 1343556 z^5 + 439040 z^6 + 61440 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (672980 + 3533145 z + 15976539 z^2 + 29879179 z^3 + 31684341 z^4 + 19725696 z^5 + 6748160 z^6 + 983040 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (422463195 Pi z^2 Sqrt[1 + Sqrt[1 + z]])

Standard Form

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MathML Form

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<sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]