Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0639)

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=9/2

http://functions.wolfram.com/07.22.03.0639.01

Input Form

HypergeometricPFQ[{-(11/2)}, {9/2, 5}, z] == (4 (2 Sqrt[z] (11588006707200 + 45155168826075 z + 50885743293000 z^2 + 100491856264800 z^3 - 59785980612480 z^4 + 7110985688064 z^5 - 289979099136 z^6 + 4722892800 z^7 - 30834688 z^8 + 65536 z^9) BesselI[0, 2 Sqrt[z]] - (23176013414400 + 67868800686225 z + 70130324880000 z^2 + 75718746734400 z^3 - 56464322711040 z^4 + 6969992283648 z^5 - 287644336128 z^6 + 4707532800 z^7 - 30801920 z^8 + 65536 z^9) BesselI[1, 2 Sqrt[z]]) - Pi Sqrt[z] (102088631019375 + 245012714446500 z + 261346895409600 z^2 + 348462527212800 z^3 - 232308351475200 z^4 + 28158588057600 z^5 - 1155224125440 z^6 + 18860802048 z^7 - 123273216 z^8 + 262144 z^9) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi Sqrt[z] (102088631019375 + 245012714446500 z + 261346895409600 z^2 + 348462527212800 z^3 - 232308351475200 z^4 + 28158588057600 z^5 - 1155224125440 z^6 + 18860802048 z^7 - 123273216 z^8 + 262144 z^9) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])/(386174921932800 z^(7/2))

Standard Form

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MathML Form

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type='integer'> 261346895409600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 245012714446500 </cn> <ci> z </ci> </apply> <cn type='integer'> 102088631019375 </cn> </apply> <apply> <ci> BesselI </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> <ci> StruveL </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> <apply> <times /> <pi /> <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'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 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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]