Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0524)

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

For fixed z and a₁=-11/2, b₁=1/2

http://functions.wolfram.com/07.22.03.0524.01

Input Form

HypergeometricPFQ[{-(11/2)}, {1/2, 6}, -z] == -((1/(13749310575 z^(9/2))) (2 (-4 (2 Sqrt[z] (-1768189500 - 147349125 z - 98232750 z^2 - 104781600 z^3 + 628689600 z^4 + 3846769920 z^5 + 1808603685 z^6 + 189591120 z^7 + 6338592 z^8 + 73984 z^9 + 256 z^10) BesselJ[0, 2 Sqrt[z]] - (-3536379000 + 1473491250 z + 245581875 z^2 - 13097700 z^3 - 314344800 z^4 + 3083149440 z^5 + 1719032175 z^6 + 186485400 z^7 + 6301824 z^8 + 73856 z^9 + 256 z^10) BesselJ[1, 2 Sqrt[z]]) - Pi z^(11/2) (13749310575 + 7050928500 z + 752099040 z^2 + 25280640 z^3 + 295680 z^4 + 1024 z^5) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] + Pi z^(11/2) (13749310575 + 7050928500 z + 752099040 z^2 + 25280640 z^3 + 295680 z^4 + 1024 z^5) BesselJ[0, 2 Sqrt[z]] StruveH[1, 2 Sqrt[z]])))

Standard Form

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MathML Form

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</annotation-xml> </semantics> </math>

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]