Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0573)

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=2

http://functions.wolfram.com/07.22.03.0573.01

Input Form

HypergeometricPFQ[{-(11/2)}, {2, 7/2}, z] == (1/(1487842836480 z^2)) (4 (2 z (1404728325 + 242902085580 z - 452368414512 z^2 + 142972132032 z^3 - 12886759680 z^4 + 407077888 z^5 - 4689920 z^6 + 16384 z^7) BesselI[0, 2 Sqrt[z]] - Sqrt[z] (4214184975 + 99983475900 z - 390536095824 z^2 + 136864527552 z^3 - 12687250176 z^4 + 404747264 z^5 - 4681728 z^6 + 16384 z^7) BesselI[1, 2 Sqrt[z]]) + Pi (4214184975 - 44951306400 z - 629318289600 z^2 + 1678182105600 z^3 - 559394035200 z^4 + 51144597504 z^5 - 1623638016 z^6 + 18743296 z^7 - 65536 z^8) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (-4214184975 + 44951306400 z + 629318289600 z^2 - 1678182105600 z^3 + 559394035200 z^4 - 51144597504 z^5 + 1623638016 z^6 - 18743296 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'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 629318289600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 44951306400 </cn> <ci> z </ci> </apply> <cn type='integer'> -4214184975 </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]