Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0653)

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=11/2

http://functions.wolfram.com/07.22.03.0653.01

Input Form

HypergeometricPFQ[{-(11/2)}, {11/2, 6}, z] == (4 (2 Sqrt[z] (1854081073152000 + 5658623250674625 z + 4433938513042500 z^2 + 2230034310504000 z^3 + 2241691682630400 z^4 - 905534781903360 z^5 + 76383839508480 z^6 - 2317700874240 z^7 + 29161095168 z^8 - 151453696 z^9 + 262144 z^10) BesselI[0, 2 Sqrt[z]] - (3708162146304000 + 8168984654551875 z + 5689683120082500 z^2 + 2811427591896000 z^3 + 1846599666912000 z^4 - 869246159685120 z^5 + 75249832089600 z^6 - 2303251660800 z^7 + 29085597696 z^8 - 151322624 z^9 + 262144 z^10) BesselI[1, 2 Sqrt[z]]) - Pi Sqrt[z] (15007028759848125 + 28584816685425000 z + 20581068013506000 z^2 + 10453875816384000 z^3 + 8130792301632000 z^4 - 3547982095257600 z^5 + 303246332928000 z^6 - 9241793003520 z^7 + 116493189120 z^8 - 605552640 z^9 + 1048576 z^10) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi Sqrt[z] (15007028759848125 + 28584816685425000 z + 20581068013506000 z^2 + 10453875816384000 z^3 + 8130792301632000 z^4 - 3547982095257600 z^5 + 303246332928000 z^6 - 9241793003520 z^7 + 116493189120 z^8 - 605552640 z^9 + 1048576 z^10) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])/(7208598542745600 z^(9/2))

Standard Form

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MathML Form

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type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9241793003520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 303246332928000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3547982095257600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 8130792301632000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10453875816384000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 20581068013506000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 28584816685425000 </cn> <ci> z </ci> </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]