Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a86g)

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=-21/4, b>=a

For fixed z and a=-21/4, b=-19/4

http://functions.wolfram.com/07.23.03.a86g.01

Input Form

Hypergeometric2F1[-(21/4), -(19/4), 5, z] == (1/(834833040166125 Pi z^4)) (4096 Sqrt[1 + Sqrt[z]] ((-1612416 + 43199312 z - 687355305 z^2 + 11216809695 z^3 + 678746586915 z^4 + 2625546653307 z^5 + 2806781948901 z^6 + 940501302045 z^7 + 83786181345 z^8 + 891866745 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + 16 (100776 - 100776 Sqrt[z] - 2624375 z + 2624375 z^(3/2) + 41003235 z^2 - 41003235 z^(5/2) - 670601295 z^3 + 670601295 z^(7/2) - 17442838125 z^4 + 17442838125 z^(9/2) - 48596369517 z^5 + 48596369517 z^(11/2) - 36768618495 z^6 + 36768618495 z^(13/2) - 7888590285 z^7 + 7888590285 z^(15/2) - 340611615 z^8 + 340611615 z^(17/2)) 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]