Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9003)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.9003.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, -(23/4)}, -z] == ((-4 z (23166108458868375 + 1058746921293600 z - 3317522726246400 z^2 + 541216650240000 z^3 - 37969141432320 z^4 + 1498643693568 z^5 - 36641439744 z^6 + 536870912 z^7) BesselJ[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (38610180764780625 + 2597201348742000 z - 1930190921971200 z^2 + 288465582182400 z^3 - 19669037875200 z^4 + 765748838400 z^5 - 18555600896 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-579152711471709375 + 12522220788577500 z - 16999863373584000 z^2 + 15065686521446400 z^3 - 2285168578560000 z^4 + 156523246387200 z^5 - 6106613022720 z^6 + 148176371712 z^7 - 2147483648 z^8) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(5117567057479800 Sqrt[2] z^(9/4))

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]