Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4qb)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-47/8, b>=a

For fixed z and a=-47/8, b=-29/8

http://functions.wolfram.com/07.23.03.b4qb.01

Input Form

Hypergeometric2F1[-(47/8), -(29/8), 6, z] == (524288 2^(1/4) (-2 Sqrt[1 - z] (-620658688 + 14214538624 z - 174943981719 z^2 + 1695784377443 z^3 - 18913264409585 z^4 - 419342959416945 z^5 - 911110822222315 z^6 - 513458666608535 z^7 - 69720005239755 z^8 - 341610661275 z^9 + 6764567550 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-620658688 + 14214538624 z - 174943981719 z^2 + 1695784377443 z^3 - 18913264409585 z^4 - 419342959416945 z^5 - 911110822222315 z^6 - 513458666608535 z^7 - 69720005239755 z^8 - 341610661275 z^9 + 6764567550 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (-620658688 + 14214538624 z - 174943981719 z^2 + 1695784377443 z^3 - 18913264409585 z^4 - 419342959416945 z^5 - 911110822222315 z^6 - 513458666608535 z^7 - 69720005239755 z^8 - 341610661275 z^9 + 6764567550 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-620658688 + 14602450304 z - 183764426599 z^2 + 1803696652628 z^3 - 19955856128260 z^4 + 600699404905400 z^5 + 2884823299348310 z^6 + 3187664725081040 z^7 + 1004659878426620 z^8 + 66536286421800 z^9 - 690662346855 z^10 + 13529135100 z^11) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (264342720386660270355 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^5)

Standard Form

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MathML Form

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</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]