Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8039)

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/07.22.03.8039.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(9/2), 21/4}, -z] == (221 (Sqrt[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) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-39293319563212089375 + 28095443145564102000 z + 528264986578560000 z^2 + 124405260908544000 z^3 - 33485647645900800 z^4 + 3982454371123200 z^5 - 293362036899840 z^6 + 16508780544000 z^7 - 923417968640 z^8 - 68719476736 z^9) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-13097773187737363125 + 1381743105519546000 z - 50768323385472000 z^2 - 93181979739340800 z^3 + 29712524289638400 z^4 - 3726563239526400 z^5 + 280336206397440 z^6 - 15993384468480 z^7 + 974957576192 z^8 + 68719476736 z^9) Sin[2 Sqrt[z]])))/ (335152254769378099200 z^(17/4))

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]