Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2006
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2006

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

Search the Archive

Re: Troubles with Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70236] Re: Troubles with Integrate
  • From: dimmechan at yahoo.com
  • Date: Sun, 8 Oct 2006 02:05:02 -0400 (EDT)
  • References: <eg84hk$nir$1@smc.vnet.net>

Hello Roman.

$VersionNumber
5.2

psi = -(((Sin[(1/3)*Pi*(t - 5/4)]*Cos[Pi*(t - 5/4)])/(t - 5/4) +
(Sin[Pi*(t + 1/4)]*Cos[Pi*(t + 1/4)])/(t + 1/4))/Pi) +
   ((Sin[(2/3)*Pi*(t - 7/8)]*Sin[2*Pi*(t - 7/8)])/(t - 7/8) -
(Sin[(2/3)*Pi*(t - 1/8)]*Sin[2*Pi*(t - 1/8)])/(t - 1/8))/Pi;

First of all as regards the integral of psi over
{t,-infinitty,infinity} I think Mathematica 5.2
is right.

Integrate[psi, t]
(1/Pi)*((1/2)*CosIntegral[(1/6)*Pi*(-7 + 8*t)] -
(1/2)*CosIntegral[(1/3)*Pi*(-7 + 8*t)] -
   (1/2)*CosIntegral[(1/6)*(Pi - 8*Pi*t)] + (1/2)*CosIntegral[(1/3)*(Pi
- 8*Pi*t)] - (1/2)*SinIntegral[(1/6)*Pi*(5 - 4*t)] +
   (1/2)*SinIntegral[(1/3)*Pi*(5 - 4*t)] - (1/2)*SinIntegral[Pi/2 +
2*Pi*t])

Timing[Integrate[psi, {t, -Infinity, Infinity}]]
{36.437999999999995*Second, -(1/2)}

Timing[NIntegrate[psi3, {t, -Infinity, Infinity}, Method ->
DoubleExponential,
 MaxRecursion -> 16]]
NIntegrate::slwcon :(...)
NIntegrate::ncvi :(...)
{33.827999999999975*Second, -0.5089996793160453}

Second I din't get the error message you mention to your post (no
matter how I tried!).

I hope someone will help you to evaluate the integral of psi^2 over {t,
-Infinity, Infinity}.
I failed to evalute it even I try two or three approaches.

I believe you cannot obtain a closed form result, but I wish I do
mistake.

Here is a numerical approxiamation:

Timing[NIntegrate[psi^2, {t, -Infinity, Infinity}, MaxRecursion -> 20]]
(messages are not displayed)
{17.046999999999997*Second, 0.9331917391109911}


  • Prev by Date: Re: Problem with nested NIntegrate[]
  • Next by Date: Re: How to assign the result from NonlinearFit to a function
  • Previous by thread: Re: Troubles with Integrate
  • Next by thread: Re: Troubles with Integrate