Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a87d)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.a87d.01

Input Form

HypergeometricPFQ[{-(15/4)}, {3/2, 23/4}, -z] == (19 (2 Sqrt[z] (23283371986875 - 10370908548000 z - 2911132224000 z^2 + 1976041267200 z^3 + 237095623065600 z^4 + 169299777945600 z^5 + 19590587351040 z^6 + 582504939520 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - (69850115960625 - 137550997584000 z - 36521476992000 z^2 - 13549997260800 z^3 + 158083301376000 z^4 + 157984122470400 z^5 + 19233735966720 z^6 + 579820584960 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-69850115960625 - 11462583132000 z - 10638865036800 z^2 - 17784371404800 z^3 + 201431030169600 z^4 + 164621765836800 z^5 + 19446638837760 z^6 + 581431197696 z^7 + 4294967296 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(6637269653913600 Sqrt[2] z^(17/4))

Standard Form

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MathML Form

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169299777945600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 237095623065600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1976041267200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2911132224000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10370908548000 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 23283371986875 </cn> </apply> <apply> <power /> <apply> <ci> BesselJ </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2 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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]