Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9637)

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/07.22.03.9637.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, -(13/4)}, -z] == ((4 z (973450255498875 + 53831350534500 z + 18808606555200 z^2 + 15875448652800 z^3 - 6050366668800 z^4 + 893288448000 z^5 - 89485475840 z^6 + 11878268928 z^7 + 536870912 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (2920350766496625 - 394763237253000 z - 3231434606400 z^2 + 11105279539200 z^3 - 3406679654400 z^4 + 481461534720 z^5 - 48003809280 z^6 + 5771362304 z^7 + 268435456 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (8761052299489875 - 2853061578328500 z + 129195241282800 z^2 + 40275851616000 z^3 + 71784882892800 z^4 - 25282006548480 z^5 + 3677245931520 z^6 - 368981311488 z^7 + 46976204800 z^8 + 2147483648 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(29298256416000 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]