Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7981)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.7981.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(11/2), 11/4}, -z] == ((2 Sqrt[z] (-229269753838125 + 471847149774000 z - 290097793440000 z^2 + 50697845452800 z^3 - 4395943526400 z^4 + 233145630720 z^5 - 8640266240 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]]^2 + (687809261514375 - 885455601030000 z + 334149719904000 z^2 - 53979338649600 z^3 + 4559295283200 z^4 - 238996684800 z^5 + 8808038400 z^6 - 268435456 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (687809261514375 + 581870823534000 z - 305168127264000 z^2 + 51908813107200 z^3 - 4458099179520 z^4 + 235410554880 z^5 - 8707375104 z^6 + 268435456 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(1052117434368000 Sqrt[2] z^(5/4))

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]