Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0654)

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/07.22.03.0654.01

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) BesselJ[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) BesselJ[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) BesselJ[1, 2 Sqrt[z]] StruveH[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) BesselJ[0, 2 Sqrt[z]] StruveH[1, 2 Sqrt[z]])/(7208598542745600 z^(9/2))

Standard Form

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MathML Form

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8130792301632000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10453875816384000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 20581068013506000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 28584816685425000 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 15007028759848125 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mi> J </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <mstyle fontweight='bold' fontstyle='normal'> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> StruveH </ci> </annotation-xml> </semantics> </mstyle> <mn> 1 </mn> </msub> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 7208598542745600 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </list> <list> <cn type='rational'> 11 <sep /> 2 </cn> <cn type='integer'> 6 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 262144 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 151453696 </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]