Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1227)

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=1

http://functions.wolfram.com/07.22.03.1227.01

Input Form

HypergeometricPFQ[{-(7/2)}, {1, 11/2}, z] == (1/(587202560 z^4)) (4 (2 z (-40516875 + 15655500 z - 8996400 z^2 + 83348160 z^3 - 166545664 z^4 + 35521536 z^5 - 1609728 z^6 + 16384 z^7) BesselI[0, 2 Sqrt[z]] + Sqrt[z] (121550625 - 25357500 z + 17816400 z^2 - 24696000 z^3 + 150119168 z^4 - 34731008 z^5 + 1601536 z^6 - 16384 z^7) BesselI[1, 2 Sqrt[z]]) + Pi (-121550625 + 79380000 z - 44452800 z^2 + 39513600 z^3 - 197568000 z^4 + 632217600 z^5 - 140492800 z^6 + 6422528 z^7 - 65536 z^8) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (121550625 - 79380000 z + 44452800 z^2 - 39513600 z^3 + 197568000 z^4 - 632217600 z^5 + 140492800 z^6 - 6422528 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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<times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 79380000 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 121550625 </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]