Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8324)

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/07.22.03.8324.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, 19/4}, z] == ((2 Sqrt[z] (-27393782656865625 + 10751960869650000 z - 40477970332800000 z^2 + 5143879215820800000 z^3 - 6439472668223078400 z^4 + 1453883749407129600 z^5 - 99456499109068800 z^6 + 2490179088547840 z^7 - 23471996272640 z^8 + 68719476736 z^9) BesselI[-(1/4), Sqrt[z]]^2 + (82181347970596875 + 92972838108150000 z - 16191188133120000 z^2 - 2720119606364160000 z^3 + 5672310286919270400 z^4 - 1395643830239232000 z^5 + 97938763363123200 z^6 - 2475624518123520 z^7 + 23429046599680 z^8 - 68719476736 z^9) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (82181347970596875 - 82347370895790000 z + 186198663530880000 z^2 + 3958155973236326400 z^3 - 6110682865149542400 z^4 + 1429950424154112000 z^5 - 98842996585267200 z^6 + 2484337933025280 z^7 - 23454816403456 z^8 + 68719476736 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (8275845599723520000 Sqrt[2] 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]