Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1680)

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=-5/2, b_1`>=-11/2

For fixed z and a₁=-5/2, b₁=11/2

http://functions.wolfram.com/07.22.03.1680.01

Input Form

HypergeometricPFQ[{-(5/2)}, {11/2, 6}, -z] == (1/(184504320 z^(9/2))) (4 (2 Sqrt[z] (464486400 - 909879075 z + 464902200 z^2 - 146739600 z^3 + 75905280 z^4 + 15858432 z^5 + 538624 z^6 + 4096 z^7) BesselJ[0, 2 Sqrt[z]] - (928972800 - 1220056425 z + 556189200 z^2 - 173048400 z^3 + 68428800 z^4 + 15592704 z^5 + 536576 z^6 + 4096 z^7) BesselJ[1, 2 Sqrt[z]]) + Pi Sqrt[z] (3192564375 - 4256752500 z + 2043241200 z^2 - 648648000 z^3 + 288288000 z^4 + 62899200 z^5 + 2150400 z^6 + 16384 z^7) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi Sqrt[z] (3192564375 - 4256752500 z + 2043241200 z^2 - 648648000 z^3 + 288288000 z^4 + 62899200 z^5 + 2150400 z^6 + 16384 z^7) BesselJ[0, 2 Sqrt[z]] StruveH[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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</cn> </apply> </apply> </apply> <apply> <ci> StruveH </ci> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </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]