Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2007
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2007

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Integrating SphericalHarmonicY

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73199] Re: Integrating SphericalHarmonicY
  • From: dh <dh at metrohm.ch>
  • Date: Wed, 7 Feb 2007 05:26:20 -0500 (EST)
  • References: <eq9c4v$n37$1@smc.vnet.net>


Hi,

if you want to define a rule for this integral for symbolic l and m, you 

may define an Upvalue for e.g. Integrate:

Unprotect[Integrate]

Integrate[Conjugate[SphericalHarmonicY[l_, m_, theta_, phi_]] 

SphericalHarmonicY[l_, m_, theta_, phi_] Sin[theta_], {theta_, 0, Pi}, 

{phi, 0, 2 Pi}] = 1

from now on this integral evaluates to 1.

Daniel



wgempel at yahoo.com wrote:

> I would like

> 

> Integrate[

>     Conjugate[SphericalHarmonicY[l,m,theta,phi]]

>     SphericalHarmonicY[l,m,theta,phi] Sin[theta],

>     {theta, 0, Pi}, {phi, 0, 2 Pi}]

> 

> to evaluate to 1 (without having to force it through a rule every

> time).

> 

> I have tried

> $Assumptions =

>     {Element[Alternatives[theta,phi], Reals] &&

>      Element[Alternatives[l,m], Integers] &&

>      l >= Abs[m]}

> 

> Thanks for any help.

> 




  • Prev by Date: Re: String to number
  • Next by Date: Re: String to number
  • Previous by thread: Integrating SphericalHarmonicY
  • Next by thread: Re: Integrating SphericalHarmonicY