Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8e0)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.a8e0.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(11/2), 23/4}, z] == (19 (4 z^(1/4) (-341435127939530625 - 455246837252707500 Sqrt[z] - 293134548865158000 z - 113362278637608000 z^(3/2) - 26471845701100800 z^2 - 3356788340505600 z^(5/2) - 173197308211200 z^3 + 86826055680000 z^(7/2) - 10768343040000 z^4 + 40465466130432 z^(9/2) - 781420855296 z^5 + 3054111817728 z^(11/2) - 22934454272 z^6 + 90932510720 z^(13/2) - 268435456 z^7 + 1073741824 z^(15/2) + E^(4 Sqrt[z]) (341435127939530625 - 455246837252707500 Sqrt[z] + 293134548865158000 z - 113362278637608000 z^(3/2) + 26471845701100800 z^2 - 3356788340505600 z^(5/2) + 173197308211200 z^3 + 86826055680000 z^(7/2) + 10768343040000 z^4 + 40465466130432 z^(9/2) + 781420855296 z^5 + 3054111817728 z^(11/2) + 22934454272 z^6 + 90932510720 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (341435127939530625 - 71062920937008000 z + 9777699195264000 z^2 - 1354486468608000 z^3 + 311376199680000 z^4 + 159424614236160 z^5 + 12146637275136 z^6 + 362924736512 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (341435127939530625 - 71062920937008000 z + 9777699195264000 z^2 - 1354486468608000 z^3 + 311376199680000 z^4 + 159424614236160 z^5 + 12146637275136 z^6 + 362924736512 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(23643898043695104 z^(19/4))

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,a₂},{b₁},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]