Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a90k)

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=-19/4, b>=a

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

http://functions.wolfram.com/07.23.03.a90k.01

Input Form

Hypergeometric2F1[-(19/4), -(19/4), 5, z] == (1/(31627707093675 Pi z^4)) (4096 (4 Sqrt[1 - z] (-40128 + 1001528 z - 14818727 z^2 + 225322482 z^3 + 6703623815 z^4 + 18636521428 z^5 + 13718662167 z^6 + 2783551202 z^7 + 106611433 z^8) EllipticE[(1/2) (1 - Sqrt[1 - z])] - 2 Sqrt[1 - z] (-40128 + 1001528 z - 14818727 z^2 + 225322482 z^3 + 6703623815 z^4 + 18636521428 z^5 + 13718662167 z^6 + 2783551202 z^7 + 106611433 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])] + (80256 - 2063248 z + 31134103 z^2 - 472734801 z^3 + 2371931555 z^4 + 41535474379 z^5 + 78467006373 z^6 + 40779322637 z^7 + 5790768481 z^8 + 140821065 z^9) EllipticK[(1/2) (1 - 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]