Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0971)

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=4

http://functions.wolfram.com/07.22.03.0971.01

Input Form

HypergeometricPFQ[{-(9/2)}, {4, 9/2}, z] == (1/(531372441600 z^3)) (-4 (2 z (-29439164475 - 53199285300 z - 133259742000 z^2 + 84088232640 z^3 - 9773717760 z^4 + 353338368 z^5 - 4427776 z^6 + 16384 z^7) BesselI[0, 2 Sqrt[z]] + Sqrt[z] (49300635825 + 76456037700 z + 98375634000 z^2 - 79491314880 z^3 + 9600848640 z^4 - 351138816 z^5 + 4419584 z^6 - 16384 z^7) BesselI[1, 2 Sqrt[z]]) + Pi (-28733079375 - 183891708000 z - 286053768000 z^2 - 457686028800 z^3 + 326918592000 z^4 - 38745907200 z^5 + 1408942080 z^6 - 17694720 z^7 + 65536 z^8) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (28733079375 + 183891708000 z + 286053768000 z^2 + 457686028800 z^3 - 326918592000 z^4 + 38745907200 z^5 - 1408942080 z^6 + 17694720 z^7 - 65536 z^8) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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/> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9773717760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 84088232640 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 133259742000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 53199285300 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -29439164475 </cn> </apply> <apply> <ci> BesselI </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> <times /> <apply> <power /> 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<ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 286053768000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 183891708000 </cn> <ci> z </ci> </apply> <cn type='integer'> 28733079375 </cn> </apply> <apply> <ci> BesselI </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> <ci> StruveL </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> </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]