Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9661)

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/07.22.03.9661.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, 11/4}, -z] == ((2 z (4359340235250 + 5337967635000 z - 39941053977825 z^2 + 245860665336000 z^3 + 118502733024000 z^4 + 12254019747840 z^5 + 408394465280 z^6 + 4794089472 z^7 + 16777216 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - Sqrt[z] (26156041411500 + 27045702684000 z - 87937701927075 z^2 + 188319184653600 z^3 + 111476793542400 z^4 + 12006630604800 z^5 + 405426339840 z^6 + 4783603712 z^7 + 16777216 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (19617031058625 + 16547699668500 z + 48539919027600 z^2 - 142979196209850 z^3 + 440707537670400 z^4 + 231180489745920 z^5 + 24307525877760 z^6 + 814404993024 z^7 + 9579790336 z^8 + 33554432 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (322280820576000 Sqrt[2] z^(15/4))

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]