Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1265)

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=-7/2, b_1`>=-11/2

For fixed z and a₁=-7/2, b₁=2

http://functions.wolfram.com/07.22.03.1265.01

Input Form

HypergeometricPFQ[{-(7/2)}, {2, 11/2}, z] == (1/(2642411520 z^4)) (4 (2 z (52093125 - 33736500 z + 33339600 z^2 + 552565440 z^3 - 489593088 z^4 + 63734784 z^5 - 2068480 z^6 + 16384 z^7) BesselI[0, 2 Sqrt[z]] - Sqrt[z] (156279375 - 73426500 z + 80967600 z^2 + 354997440 z^3 - 459461376 z^4 + 62714880 z^5 - 2060288 z^6 + 16384 z^7) BesselI[1, 2 Sqrt[z]]) + Pi (156279375 - 142884000 z + 133358400 z^2 - 355622400 z^3 - 1778112000 z^4 + 1896652800 z^5 - 252887040 z^6 + 8257536 z^7 - 65536 z^8) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (-156279375 + 142884000 z - 133358400 z^2 + 355622400 z^3 + 1778112000 z^4 - 1896652800 z^5 + 252887040 z^6 - 8257536 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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<apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 142884000 </cn> <ci> z </ci> </apply> <cn type='integer'> -156279375 </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]