Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab1c)

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.ab1c.01

Input Form

Hypergeometric2F1[-(15/4), -(15/4), 6, -z] == (16384 Sqrt[2] ((-Sqrt[1 + z]) (67584 + 1255584 z + 12250931 z^2 + 91583646 z^3 + 762617625 z^4 - 10640456876 z^5 + 14034752949 z^6 - 4105336434 z^7 + 205811231 z^8) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - (67584 + 1323168 z + 13506515 z^2 + 103834577 z^3 + 854201271 z^4 - 9877839251 z^5 + 3394296073 z^6 + 9929416515 z^7 - 3899525203 z^8 + 205811231 z^9) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (67584 + 1255584 z + 12250931 z^2 + 91583646 z^3 + 762617625 z^4 - 10640456876 z^5 + 14034752949 z^6 - 4105336434 z^7 + 205811231 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (67584 + 1306272 z + 13187867 z^2 + 100685739 z^3 + 830483115 z^4 + 4596493699 z^5 - 27464827383 z^6 + 23316076137 z^7 - 4560437071 z^8 + 140821065 z^9) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (120185286955965 Pi z^5 Sqrt[1 + Sqrt[1 + z]])

Standard Form

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MathML Form

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</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]