Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0558)

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=3/2

http://functions.wolfram.com/07.22.03.0558.01

Input Form

HypergeometricPFQ[{-(11/2)}, {3/2, 4}, -z] == (1/(66162096000 z^(5/2))) (4 (2 Sqrt[z] (89812800 + 209563200 z + 10059033600 z^2 + 22241701575 z^3 + 7760508660 z^4 + 741140064 z^5 + 24306816 z^6 + 287488 z^7 + 1024 z^8) BesselJ[0, 2 Sqrt[z]] - (179625600 + 329313600 z + 3353011200 z^2 + 18913418325 z^3 + 7409956500 z^4 + 729233568 z^5 + 24163968 z^6 + 286976 z^7 + 1024 z^8) BesselJ[1, 2 Sqrt[z]]) + Pi z^(5/2) (23880381525 + 81875593800 z + 30324294000 z^2 + 2940537600 z^3 + 96940800 z^4 + 1148928 z^5 + 4096 z^6) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi z^(5/2) (23880381525 + 81875593800 z + 30324294000 z^2 + 2940537600 z^3 + 96940800 z^4 + 1148928 z^5 + 4096 z^6) BesselJ[0, 2 Sqrt[z]] StruveH[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 729233568 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7409956500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 18913418325 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3353011200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 329313600 </cn> <ci> z </ci> </apply> <cn type='integer'> 179625600 </cn> </apply> <apply> <ci> BesselJ </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]