Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aad6)

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=-17/4, b>=a

For fixed z and a=-17/4, b=-7/4

http://functions.wolfram.com/07.23.03.aad6.01

Input Form

Hypergeometric2F1[-(17/4), -(7/4), 5, z] == (1/(2668748457375 Pi z^4)) (4096 Sqrt[1 + Sqrt[z]] ((-84864 + 1326000 z - 11310117 z^2 + 88223421 z^3 + 1843054730 z^4 + 1893064778 z^5 + 221242175 z^6 - 9388071 z^7 + 403788 z^8) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - 2 (-42432 + 42432 Sqrt[z] + 631176 z - 631176 z^(3/2) - 5186649 z^2 + 5186649 z^(5/2) + 40293825 z^3 - 40293825 z^(7/2) + 299616790 z^4 - 299616790 z^(9/2) + 165850234 z^5 - 165850234 z^(11/2) + 2254483 z^6 - 2254483 z^(13/2) - 100947 z^7 + 100947 z^(15/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[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]