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Re: Reference of the formulas

• To: mathgroup at smc.vnet.net
• Subject: [mg123867] Re: Reference of the formulas
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sat, 24 Dec 2011 07:08:21 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201112231212.HAA01818@smc.vnet.net>

Can't you just cite Mathematica and/or functions.wolfram.com?

Integrate[(z^\[Nu] BesselK[\[Nu],a z])/E^(a z),z]==(1/(1+2 \[Nu]))
(z^\[Nu] ((z (-BesselK[-1-\[Nu],a z]+BesselK[\[Nu],a z]))/E^(a
z)-(2^\[Nu] Pi Csc[Pi \[Nu]])/((a z)^\[Nu] (a
Gamma[-\[Nu]]))))//FullSimplify

True

Wolfram Research, Inc., Mathematica, Version 8.0, Champaign, IL (2010).
http://functions.wolfram.com/03.04.21.0023.01

Integrate[(z^(\[Alpha]-1) BesselK[\[Nu],a z^r])/E^(a
z^r),z]==(2^(-1-\[Nu]) z^\[Alpha] ((1/(\[Alpha]-r \[Nu])) (4^\[Nu]
Gamma[\[Nu]] HypergeometricPFQ[{1/2-\[Nu],\[Alpha]/r-\[Nu]},{1-2
\[Nu],1+\[Alpha]/r-\[Nu]},-2 a z^r])+(1/(\[Alpha]+r \[Nu])) ((a
z^r)^(2 \[Nu]) Gamma[-\[Nu]]
HypergeometricPFQ[{1/2+\[Nu],\[Alpha]/r+\[Nu]},{1+\[Alpha]/r+\[Nu],1+2
\[Nu]},-2 a z^r])))/(a z^r)^\[Nu]//FullSimplify

True

Wolfram Research, Inc., Mathematica, Version 8.0, Champaign, IL (2010).
http://functions.wolfram.com/03.04.21.0027.01


Bob Hanlon

On Fri, Dec 23, 2011 at 7:12 AM, Mehdi Mortazawi
<mehdimortazawi at gmail.com> wrote:
> Hi,
> I have used some formulas for my calculations.
> actually these two integrations:
>
> http://functions.wolfram.com/Bessel-TypeFunctions/BesselK/21/01/02/03/01/01/0003/
> http://functions.wolfram.com/Bessel-TypeFunctions/BesselK/21/01/02/03/01/02/0001/
>
> for writing a paper, I need a reference for the formulas. I searched
> the references in
>
> http://mathworld.wolfram.com/ModifiedBesselFunctionoftheSecondKind.html
>
> and also the the following book: "Table of Integrals, Series and
> products, 7th ed. by Gradshteyn and Ryzhic"
>
> but no luck yet.
> can anybody help me finding a paper/book about the mentioned
> integration.
>

• References:
  • Reference of the formulas
    • From: Mehdi Mortazawi <mehdimortazawi@gmail.com>