Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9087)

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=-17/4

http://functions.wolfram.com/07.23.03.9087.01

Input Form

Hypergeometric2F1[-(23/4), -(17/4), 4, -z] == -((1/(157941385977375 Pi z^3)) (256 (1 + z)^(1/4) ((67990208 + 2143816246 z + 51831910130 z^2 - 4250303996610 z^3 + 20069002876650 z^4 - 24786192623934 z^5 + 9037393946742 z^6 - 768449053110 z^7 + 212458350 z^8) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + (-33995104 (1 + Sqrt[1 + z]) + 106229175 z^8 (-1 + 2 Sqrt[1 + z]) - 37182145 z^2 (697 + 676 Sqrt[1 + z]) - 1062347 z (1009 + 985 Sqrt[1 + z]) + 15 z^7 (25614968437 + 1409307055 Sqrt[1 + z]) - 525 z^4 (19113336073 + 5912940242 Sqrt[1 + z]) + 105 z^3 (20239542841 + 8666334623 Sqrt[1 + z]) - 21 z^6 (215176046351 + 29208116960 Sqrt[1 + z]) + 21 z^5 (590147443427 + 128451657167 Sqrt[1 + z])) EllipticK[1/2 - 1/(2 Sqrt[1 + z])])))

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]