Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9673)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9673.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, 23/4}, -z] == ((2 Sqrt[z] (14057774639086303125 - 30593255477254470000 z + 20610396942879744000 z^2 - 9786820319461785600 z^3 + 14959476551467008000 z^4 + 3369796197993676800 z^5 + 188568882213027840 z^6 + 3775958079242240 z^7 + 28694676504576 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]]^2 - (42173323917258909375 - 57173444679741390000 z + 31989634359306624000 z^2 - 15171332345538969600 z^3 + 13130407234938470400 z^4 + 3257959989274214400 z^5 + 186256307068600320 z^6 + 3758139333672960 z^7 + 28651726831616 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (31979501873624930625 - 41270921672226246000 z + 25202048945904230400 z^2 - 12495933115390771200 z^3 + 14184248632256102400 z^4 + 3324077420367052800 z^5 + 187635975051018240 z^6 + 3768811253661696 z^7 + 28677496635392 z^8 + 68719476736 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (16320769526071296000 Sqrt[2] 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]