Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8995)

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=-21/4

http://functions.wolfram.com/07.23.03.8995.01

Input Form

Hypergeometric2F1[-(23/4), -(21/4), 2, -z] == (1/(5019589575 Pi z)) (8 (1 + z)^(1/4) (-2 (7436429 - 2479004562 z + 28837266915 z^2 - 78272096700 z^3 + 63654394755 z^4 - 15013304082 z^5 + 715057581 z^6) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + (7436429 (1 + Sqrt[1 + z]) + 21 z^6 (34050361 + 1221025 Sqrt[1 + z]) - 2100 z^3 (37272427 + 10255303 Sqrt[1 + z]) - 126 z^5 (119153207 + 13137547 Sqrt[1 + z]) + 105 z^4 (606232331 + 114757595 Sqrt[1 + z]) - 6 z (413167427 + 204947415 Sqrt[1 + z]) + 15 z^2 (1922484461 + 716057541 Sqrt[1 + z])) EllipticK[1/2 - 1/(2 Sqrt[1 + 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]