Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8at)

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=-11/4

http://functions.wolfram.com/07.23.03.a8at.01

Input Form

Hypergeometric2F1[-(21/4), -(11/4), 6, z] == (1/(6845630929362225 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((3168256 - 62325536 z + 643284369 z^2 - 5060133351 z^3 + 43660156449 z^4 + 1253605451061 z^5 + 2239770937527 z^6 + 882715008987 z^7 + 52795381947 z^8 - 1342494153 z^9 + 37552284 z^10) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-3168256 + 3168256 Sqrt[z] + 59949344 z - 59949344 z^(3/2) - 598693641 z^2 + 598693641 z^(5/2) + 4617999204 z^3 - 4617999204 z^(7/2) - 40264253211 z^4 + 40264253211 z^(9/2) - 447639166938 z^5 + 447639166938 z^(11/2) - 517021763103 z^6 + 517021763103 z^(13/2) - 115207140888 z^7 + 115207140888 z^(15/2) - 654035613 z^8 + 654035613 z^(17/2) + 18776142 z^9 - 18776142 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]