Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8362)

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`=5/2

http://functions.wolfram.com/07.22.03.8362.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, 9/4}, z] == (-4 (-62518011494400 + 104233730849325 Sqrt[z] - 1028024573429700 z - 454644107820000 z^(3/2) + 2176705668009600 z^2 + 155260455356160 z^(5/2) - 658804005780480 z^3 - 13916048670720 z^(7/2) + 56910077952000 z^4 + 431504424960 z^(9/2) - 1740484902912 z^5 - 4880072704 z^(11/2) + 19570622464 z^6 + 16777216 z^(13/2) - 67108864 z^7 + E^(4 Sqrt[z]) (62518011494400 + 104233730849325 Sqrt[z] + 1028024573429700 z - 454644107820000 z^(3/2) - 2176705668009600 z^2 + 155260455356160 z^(5/2) + 658804005780480 z^3 - 13916048670720 z^(7/2) - 56910077952000 z^4 + 431504424960 z^(9/2) + 1740484902912 z^5 - 4880072704 z^(11/2) - 19570622464 z^6 + 16777216 z^(13/2) + 67108864 z^7)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (229269753838125 + 5135642485974000 z - 9130031086176000 z^2 + 2675466984960000 z^3 - 228916961280000 z^4 + 6976516915200 z^5 - 78332821504 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (229269753838125 + 5135642485974000 z - 9130031086176000 z^2 + 2675466984960000 z^3 - 228916961280000 z^4 + 6976516915200 z^5 - 78332821504 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(26672964304896000 z^(3/2))

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]