Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0539)

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=1

http://functions.wolfram.com/07.22.03.0539.01

Input Form

HypergeometricPFQ[{-(11/2)}, {1, 9/2}, z] == (1/(2354388664320 z^3)) (4 (2 z (8104201875 - 9508930200 z + 312180311520 z^2 - 961349275008 z^3 + 397341232128 z^4 - 41667102720 z^5 + 1449664512 z^6 - 17858560 z^7 + 65536 z^8) BesselI[0, 2 Sqrt[z]] + Sqrt[z] (-24312605625 + 24204549600 z - 48409099200 z^2 + 793412361216 z^3 - 377698549248 z^4 + 40957599744 z^5 - 1440792576 z^6 + 17825792 z^7 - 65536 z^8) BesselI[1, 2 Sqrt[z]]) + Pi (24312605625 - 35010152100 z + 62240270400 z^2 - 580909190400 z^3 + 3485455142400 z^4 - 1549091174400 z^5 + 165236391936 z^6 - 5780865024 z^7 + 71368704 z^8 - 262144 z^9) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (-24312605625 + 35010152100 z - 62240270400 z^2 + 580909190400 z^3 - 3485455142400 z^4 + 1549091174400 z^5 - 165236391936 z^6 + 5780865024 z^7 - 71368704 z^8 + 262144 z^9) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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580909190400 </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'> 62240270400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 35010152100 </cn> <ci> z </ci> </apply> <cn type='integer'> -24312605625 </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]