Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8038)

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`=-9/2

http://functions.wolfram.com/07.22.03.8038.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(9/2), 21/4}, z] == -((221 (-4 z^(1/4) (-39293319563212089375 - 52391092750949452500 Sqrt[z] - 28095443145564102000 z - 5526972422078184000 z^(3/2) + 528264986578560000 z^2 - 203073293541888000 z^(5/2) - 124405260908544000 z^3 + 372727918957363200 z^(7/2) - 33485647645900800 z^4 + 118850097158553600 z^(9/2) - 3982454371123200 z^5 + 14906252958105600 z^(11/2) - 293362036899840 z^6 + 1121344825589760 z^(13/2) - 16508780544000 z^7 + 63973537873920 z^(15/2) - 923417968640 z^8 + 3899830304768 z^(17/2) + 68719476736 z^9 - 274877906944 z^(19/2) + E^(4 Sqrt[z]) (-39293319563212089375 + 52391092750949452500 Sqrt[z] - 28095443145564102000 z + 5526972422078184000 z^(3/2) + 528264986578560000 z^2 + 203073293541888000 z^(5/2) - 124405260908544000 z^3 - 372727918957363200 z^(7/2) - 33485647645900800 z^4 - 118850097158553600 z^(9/2) - 3982454371123200 z^5 - 14906252958105600 z^(11/2) - 293362036899840 z^6 - 1121344825589760 z^(13/2) - 16508780544000 z^7 - 63973537873920 z^(15/2) - 923417968640 z^8 - 3899830304768 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-39293319563212089375 + 13817431055195460000 z - 3565788659405280000 z^2 + 1126965304700928000 z^3 - 1371957762244608000 z^4 - 462133140966604800 z^5 - 58683573456076800 z^6 - 4434177923481600 z^7 - 253381595627520 z^8 - 15805479649280 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-39293319563212089375 + 13817431055195460000 z - 3565788659405280000 z^2 + 1126965304700928000 z^3 - 1371957762244608000 z^4 - 462133140966604800 z^5 - 58683573456076800 z^6 - 4434177923481600 z^7 - 253381595627520 z^8 - 15805479649280 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)]))/ E^(2 Sqrt[z])/(1340609019077512396800 z^(17/4)))

Standard Form

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MathML 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]