Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab14)

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=-15/4, b>=a

For fixed z and a=-15/4, b=-15/4

http://functions.wolfram.com/07.23.03.ab14.01

Input Form

Hypergeometric2F1[-(15/4), -(15/4), 4, -z] == (256 Sqrt[2] ((-Sqrt[1 + z]) (12320 + 273735 z + 4487175 z^2 - 115440602 z^3 + 230653998 z^4 - 94793373 z^5 + 6362747 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (12320 + 286055 z + 4760910 z^2 - 110953427 z^3 + 115213396 z^4 + 135860625 z^5 - 88430626 z^6 + 6362747 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (12320 + 273735 z + 4487175 z^2 - 115440602 z^3 + 230653998 z^4 - 94793373 z^5 + 6362747 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (12320 + 282975 z + 4691610 z^2 + 27484873 z^3 - 338216916 z^4 + 424019169 z^5 - 113110342 z^6 + 4542615 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (17866104795 Pi z^3 Sqrt[1 + Sqrt[1 + z]])

Standard Form

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MathML Form

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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]