Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8318)

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/07.22.03.8318.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, 13/4}, z] == (-4 z^(1/4) (-118587803709375 - 158117071612500 Sqrt[z] + 885455601030000 z - 10917005701694400 z^(3/2) - 5914514910124800 z^2 + 28717284700339200 z^(5/2) + 2219865590476800 z^3 - 9444047851929600 z^(7/2) - 208669400432640 z^4 + 853905219256320 z^(9/2) + 6664586526720 z^5 - 26886348472320 z^(11/2) - 76923535360 z^6 + 308499447808 z^(13/2) + 268435456 z^7 - 1073741824 z^(15/2) + E^(4 Sqrt[z]) (-118587803709375 + 158117071612500 Sqrt[z] + 885455601030000 z + 10917005701694400 z^(3/2) - 5914514910124800 z^2 - 28717284700339200 z^(5/2) + 2219865590476800 z^3 + 9444047851929600 z^(7/2) - 208669400432640 z^4 - 853905219256320 z^(9/2) + 6664586526720 z^5 + 26886348472320 z^(11/2) - 76923535360 z^6 - 308499447808 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-118587803709375 + 1011949258320000 z + 56669158465920000 z^2 - 120894204727296000 z^3 + 38379112611840000 z^4 - 3435333156864000 z^5 + 107775157862400 z^6 - 1234803097600 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-118587803709375 + 1011949258320000 z + 56669158465920000 z^2 - 120894204727296000 z^3 + 38379112611840000 z^4 - 3435333156864000 z^5 + 107775157862400 z^6 - 1234803097600 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(313943855726592000 z^(9/4))

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]