## 65 Reputation

2 years, 257 days

## Factor in matrix form...

Maple 2022

How can I  change eq13 to eq14 without using op command manually?

## Integration of Hermite to Laguerre...

Maple 2022

How  to make the integration

into the following form:

## How to find the normalization factor ?...

Maple

SolnforOS_dsolve.mw
I would like to solve eq6 in terms of sigma and n. I would appreciate for your help.

## How to find the solutions matrix(array)...

Maple 2021

How to find Z(t) matrix(array) =[ [z[1,0](t),z[1,1](t)],[z[2,0](t),z[2,1](t)]]

 > restart;
 > with(IntegrationTools):with(Physics):
 >
 >
 >
 > h1 := (m,n)->(n+1/2)*KroneckerDelta[n,m];
 (1)
 > h2 := (mu,nu,m2,l)->-(nu*Pi/l)^2/(2*m2)*KroneckerDelta[mu,nu];
 (2)
 > v1 := (m,n,m1)->sqrt(min(n,m)!/max(n,m)!)*(2*m1)^(-abs(n-m)/2)*exp(-1/(4*m1))*LaguerreL(min(n,m),abs(n-m),-1/(2*m1));
 (3)
 > v2 := (mu,nu,l)->4*Pi^2*l*mu*nu*(exp(l/2)-(-1)^(mu+nu)*exp(-l/2))/((Pi*(mu+nu))^2+l^2)/((Pi*(mu-nu))^2+l^2);
 (4)
 > h:=(m,n,mu,nu,m1,m2,l)->evalf(h1(m,n)+h2(mu,nu,m2,l)+v1(m,n,m1)+v2(mu,nu,l));
 (5)
 > m1:=1:m2:=1:l:=1:
 > H:= (m,n,mu,nu)->h(m,n,mu,nu,m1,m2,l);
 (6)
 > H(1,1,0,0);
 (7)
 > eq1:= diff(z(m,nu,t),t)=-I*Sum(Sum(H(m,n,mu,nu)*z(n,mu,t),n=1..N),mu=0..M);
 (8)
 >
 > zint := Array([[1,0],[0,1]]);
 (9)
 > Z:= Array(1..2,1..2);  for i from 1to 2 do     for j from 1 to 2 do         Z[i,j]:= dsolve({eq1,zint[i,j]},numeric,output=listprocedure);     end do; end do;
 >
 >

## better way to write the code for the int...

Maple 2021

how to write the code for integration of the orthogonal cosine function with nu=mu or with nu<>mu

 > restart;

 > phi:= (mu,Q2)->sqrt(2/l)*sin(mu*Pi*(Q2+l/2)/l);    # E:=mu->(Pi*mu/sqrt(2)/l)^2, mu=1,2...
 (1)
 > fh1:=simplify((-1/2/m2*Int(diff(phi(mu,Q2),Q2)*diff(phi(nu,Q2),Q2),Q2=-l/2..l/2)))
 (2)
 > convert(fh1,int) assuming(mu,integer,nu,integer);
 (3)
 > fh1_subs := simplify(subs(nu = mu, fh1));
 (4)
 > convert(fh1_substituted,int)assuming (mu,integer,nu,integer);
 (5)
 >