Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9264)

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=-9/4

http://functions.wolfram.com/07.23.03.9264.01

Input Form

Hypergeometric2F1[-(23/4), -(9/4), 5, z] == (1/(70801310955375 Pi z^4)) (4096 Sqrt[1 + Sqrt[z]] ((-615296 + 12382832 z - 141253695 z^2 + 1550209430 z^3 + 52834775175 z^4 + 99921358992 z^5 + 34708402911 z^6 + 100278750 z^7 - 7309575 z^8 + 331500 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - 4 (-153824 + 153824 Sqrt[z] + 2980340 z - 2980340 z^(3/2) - 33096195 z^2 + 33096195 z^(5/2) + 363072710 z^3 - 363072710 z^(7/2) + 4834509225 z^4 - 4834509225 z^(9/2) + 5744123658 z^5 - 5744123658 z^(11/2) + 943863375 z^6 - 943863375 z^(13/2) - 47503950 z^7 + 47503950 z^(15/2) + 3530475 z^8 - 3530475 z^(17/2) - 165750 z^9 + 165750 z^(19/2)) 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]