Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8322)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.8322.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, 17/4}, z] == (-4 z^(1/4) (7471031633690625 + 9961375511587500 Sqrt[z] - 9107543324880000 z - 18215086649760000 z^(3/2) + 56669158465920000 z^2 - 551047150028390400 z^(5/2) - 222371506306252800 z^3 + 1043444664144691200 z^(7/2) + 64719403912396800 z^4 - 272678628792729600 z^(9/2) - 5028078409482240 z^5 + 20510308376248320 z^(11/2) + 137281583185920 z^6 - 553237421752320 z^(13/2) - 1385126952960 z^7 + 5553392713728 z^(15/2) + 4294967296 z^8 - 17179869184 z^(17/2) + E^(4 Sqrt[z]) (7471031633690625 - 9961375511587500 Sqrt[z] - 9107543324880000 z + 18215086649760000 z^(3/2) + 56669158465920000 z^2 + 551047150028390400 z^(5/2) - 222371506306252800 z^3 - 1043444664144691200 z^(7/2) + 64719403912396800 z^4 + 272678628792729600 z^(9/2) - 5028078409482240 z^5 - 20510308376248320 z^(11/2) + 137281583185920 z^6 + 553237421752320 z^(13/2) - 1385126952960 z^7 - 5553392713728 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (7471031633690625 - 17076643734150000 z + 72860346599040000 z^2 + 2720119606364160000 z^3 - 4352191370182656000 z^4 + 1105318443220992000 z^5 - 82447995764736000 z^6 + 2217088961740800 z^7 - 22226455756800 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (7471031633690625 - 17076643734150000 z + 72860346599040000 z^2 + 2720119606364160000 z^3 - 4352191370182656000 z^4 + 1105318443220992000 z^5 - 82447995764736000 z^6 + 2217088961740800 z^7 - 22226455756800 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(13910127761424384000 z^(13/4))

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]