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

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=17/4, b_1`>=-11/2

For fixed z and a₁=17/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{17/4}, {11/2, -(9/4)}, -z] == (1/(49920 Sqrt[2] z^(15/4))) (7 (4 z (476974575 - 131231100 z + 14354880 z^2 - 803840 z^3 + 16384 z^4) BesselJ[-(1/4), Sqrt[z]]^2 - 12 Sqrt[z] (476974575 - 222083400 z + 34631680 z^2 - 2600960 z^3 + 98304 z^4) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (4292771175 - 2816421300 z + 649923120 z^2 - 66236160 z^3 + 3526656 z^4 - 65536 z^5) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)

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]