Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0633)

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=4

http://functions.wolfram.com/07.22.03.0633.01

Input Form

HypergeometricPFQ[{-(11/2)}, {4, 11/2}, z] == (4 (2 z (12537200300625 + 137711116966500 z + 176589478296000 z^2 + 371568925728000 z^3 - 226674877708800 z^4 + 27449453721600 z^5 - 1133796802560 z^6 + 18643222528 z^7 - 122617856 z^8 + 262144 z^9) BesselI[0, 2 Sqrt[z]] - Sqrt[z] (37611600901875 + 213810849598500 z + 245877359112000 z^2 + 277947264672000 z^3 - 213863724633600 z^4 + 26898325862400 z^5 - 1124581294080 z^6 + 18582142976 z^7 - 122486784 z^8 + 262144 z^9) BesselI[1, 2 Sqrt[z]]) - Pi (-37611600901875 + 214923433725000 z + 773724361410000 z^2 + 917006650560000 z^3 + 1283809310784000 z^4 - 880326384537600 z^5 + 108682269696000 z^6 - 4516665753600 z^7 + 74450534400 z^8 - 490209280 z^9 + 1048576 z^10) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (-37611600901875 + 214923433725000 z + 773724361410000 z^2 + 917006650560000 z^3 + 1283809310784000 z^4 - 880326384537600 z^5 + 108682269696000 z^6 - 4516665753600 z^7 + 74450534400 z^8 - 490209280 z^9 + 1048576 z^10) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])/(1445333041152000 z^4)

Standard Form

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MathML Form

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1283809310784000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 917006650560000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 773724361410000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 214923433725000 </cn> <ci> z </ci> </apply> <cn type='integer'> -37611600901875 </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> <ci> StruveL </ci> <cn type='integer'> 0 </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> <times /> <pi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 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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]