Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1669)

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=9/2

http://functions.wolfram.com/07.22.03.1669.01

Input Form

HypergeometricPFQ[{-(5/2)}, {9/2, 6}, z] == (1/(29652480 z^(9/2))) (-4 (2 Sqrt[z] (8294400 - 26956800 z - 31577175 z^2 - 15252300 z^3 - 10977120 z^4 + 2836608 z^5 - 115456 z^6 + 1024 z^7) BesselI[0, 2 Sqrt[z]] + (-16588800 + 45619200 z + 40817925 z^2 + 18729900 z^3 + 9655200 z^4 - 2779776 z^5 + 114944 z^6 - 1024 z^7) BesselI[1, 2 Sqrt[z]]) + Pi z^(3/2) (-152026875 - 145945800 z - 69498000 z^2 - 41184000 z^3 + 11232000 z^4 - 460800 z^5 + 4096 z^6) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi z^(3/2) (152026875 + 145945800 z + 69498000 z^2 + 41184000 z^3 - 11232000 z^4 + 460800 z^5 - 4096 z^6) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> 2779776 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9655200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 18729900 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 40817925 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 45619200 </cn> <ci> z </ci> </apply> <cn type='integer'> -16588800 </cn> </apply> <apply> <ci> BesselI </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> </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]