## 93 Reputation

18 years, 123 days

## Complex Integration...

Maple 13

Hi

Can you please let me about the folowing integral in Maple 13

int(sech(1/2*k*Pi)/(k^2+1)*exp(I*k*x),k=-infinity..infinity);
Is there any general precedure for finding these kind integrals

## Collecting...

Maple

Hi

I am seeking a generalized collect command in Maple to collect a expresion W

W:=mu[1]*mu[3]^3*sin(mu[1]*Pi)*cos(mu[2]*Pi)*sin(mu[3]*Pi)*cos(mu[4]*Pi)+mu[4]^3*mu[3]*cos(mu[1]*Pi)*cos(mu[2]*Pi)*sin(mu[3]*Pi)*sin(mu[4]*Pi)-mu[3]^3*mu[2]*cos(mu[1]*Pi)*sin(mu[2]*Pi)*sin(mu[3]*Pi)*cos(mu[4]*Pi)-mu[4]^3*mu[2]*cos(mu[1]*Pi)*sin(mu[2]*Pi)*cos(mu[3]*Pi)*sin(mu[4]*Pi);

to two different expresions W1 and W2 as

W1:=mu[3]*cos(mu[2]*Pi)*sin(mu[3]*Pi)-cos(mu[3]*Pi)*sin(mu[2]*Pi)*mu[2];

## Lagrangian density...

Maple
Dear friends Is there any way (or any package,...) that can be used to find the density of the Lagrangian of a PDE. For example the nonlinear Schrodinger (NLS) equation has the form I*Diff(u,t)+1/2*Diff(u,x\$2)-abs(u)^2*u=0. This PDE may be considered as the Euler equation which follows from the Lagrangian with density L , L=I/2*(conjugate(u)*Diff(u,t)-u*diff(conjugate(u),t))-1/2*abs(u)^2-1/2*abs(u)^4. Now, could anybody please let me know about any way to find L from NLS? many thanks sayed

## Definite Integral...

Maple
Hi; Is there any way to find a closed form of the following integral by maple, where theta is a real constant. cheers Sayed int(x*exp(-I*x*theta)/sinh(1/2*Pi*x),x=-infinity..infinity);

## Infinite Integral...

Maple
Hi; Is there any way to find int(x*exp(-I*x*theta)/sinh(1/2*Pi*x),x=-infinity..infinity); by maple, where theta is a real constant. cheers Sayed
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