Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0954)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=3

http://functions.wolfram.com/07.22.03.0954.01

Input Form

HypergeometricPFQ[{-(9/2)}, {3, 11/2}, -z] == (1/(1700391813120 z^4)) (4 (2 z (13408770375 + 19410791400 z - 119445308640 z^2 + 406213315200 z^3 + 283092092928 z^4 + 35200235520 z^5 + 1332731904 z^6 + 17268736 z^7 + 65536 z^8) BesselJ[0, 2 Sqrt[z]] - Sqrt[z] (40226311125 + 51081030000 z - 181679863680 z^2 + 290242310400 z^3 + 266583200256 z^4 + 34548682752 z^5 + 1324154880 z^6 + 17235968 z^7 + 65536 z^8) BesselJ[1, 2 Sqrt[z]]) + Pi (40226311125 + 68959390500 z + 220670049600 z^2 - 686529043200 z^3 + 1373058086400 z^4 + 1098446469120 z^5 + 139485265920 z^6 + 5313724416 z^7 + 69009408 z^8 + 262144 z^9) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi (40226311125 + 68959390500 z + 220670049600 z^2 - 686529043200 z^3 + 1373058086400 z^4 + 1098446469120 z^5 + 139485265920 z^6 + 5313724416 z^7 + 69009408 z^8 + 262144 z^9) BesselJ[0, 2 Sqrt[z]] StruveH[1, 2 Sqrt[z]])

Standard Form

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MathML 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]