Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0990)

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=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=5

http://functions.wolfram.com/07.22.03.0990.01

Input Form

HypergeometricPFQ[{-(9/2)}, {5, 11/2}, -z] == (1/(9033331507200 z^4)) (4 (2 z (-3074075138925 + 3900868939800 z - 2450317716000 z^2 + 2763499939200 z^3 + 1133549521920 z^4 + 90408093696 z^5 + 2374508544 z^6 + 22577152 z^7 + 65536 z^8) BesselJ[0, 2 Sqrt[z]] - Sqrt[z] (-5008404795975 + 5242213922400 z - 3149449128000 z^2 + 2266156569600 z^3 + 1090324200960 z^4 + 89240297472 z^5 + 2363277312 z^6 + 22544384 z^7 + 65536 z^8) BesselJ[1, 2 Sqrt[z]]) + Pi (3419236445625 - 17584644577500 z + 18756954216000 z^2 - 11670993734400 z^3 + 10003708915200 z^4 + 4446092851200 z^5 + 359280230400 z^6 + 9475522560 z^7 + 90243072 z^8 + 262144 z^9) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi (3419236445625 - 17584644577500 z + 18756954216000 z^2 - 11670993734400 z^3 + 10003708915200 z^4 + 4446092851200 z^5 + 359280230400 z^6 + 9475522560 z^7 + 90243072 z^8 + 262144 z^9) BesselJ[0, 2 Sqrt[z]] StruveH[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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<apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9475522560 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 359280230400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4446092851200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10003708915200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 11670993734400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 18756954216000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> 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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]