Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1283)

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=-7/2, b_1`>=-11/2

For fixed z and a₁=-7/2, b₁=5/2

http://functions.wolfram.com/07.22.03.1283.01

Input Form

HypergeometricPFQ[{-(7/2)}, {5/2, 6}, z] == (1/(91891800 z^(9/2))) (4 (2 Sqrt[z] (-4536000 + 1587600 z - 1663200 z^2 + 5644800 z^3 + 22382325 z^4 - 14273040 z^5 + 1437472 z^6 - 38144 z^7 + 256 z^8) BesselI[0, 2 Sqrt[z]] + (9072000 + 1360800 z + 982800 z^2 - 9172800 z^3 - 16343775 z^4 + 13586520 z^5 - 1418624 z^6 + 38016 z^7 - 256 z^8) BesselI[1, 2 Sqrt[z]]) - Pi z^(7/2) (34459425 + 76576500 z - 55692000 z^2 + 5712000 z^3 - 152320 z^4 + 1024 z^5) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi z^(7/2) (34459425 + 76576500 z - 55692000 z^2 + 5712000 z^3 - 152320 z^4 + 1024 z^5) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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<times /> <cn type='integer'> 16343775 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9172800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 982800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1360800 </cn> <ci> z </ci> </apply> <cn type='integer'> 9072000 </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> </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]