Getting error as invalid product/quotient. Someone help me to correct this error.

Matrix(2,1,[A[1],B[1]]):=MatrixInverse([Q[1]])*([Q[2]] )*..* MatrixInverse([Q[j]])*([Q[j+1]])* ..*MatrixInverse([Q[2 n-2]])*([Q[2 n-1]])Matrix(2,1,[A[N],B[N]]);

how to plot this equation?

4*del/(4*del+(1+del)^2*sinh(KL)^2)

Hi,
First of all I am not an expert in using Maple. 
When I execute the following code, it runs without an error:
----------------
restart;  

with(plots):

g:=(x,y)->sin(((1+x^2+y^2))*(Pi/2)) ;                                                                            

 q:=(n,k,x)->binomial(n,k)*(((1+x)/2)^k)*((1-x)/2)^(n-k) ;                                                            

  K:=(n,m,x,y)->((1+n)/2)*((1+m)/2)*sum(q(n,k,x)*sum(q(m,j,y)*int(int(g(t,u),u=2*(j/(m+1))-1..2*((j+1)/(m+1))-1),t=2*(k/(n+1))-1..2*((k+1)/(n+1))-1),j=0..m),k=0..n);                                                                      

p1:=plot3d(g(x,y),x=-1..1,y=-1..1,color=blue):                                                                       p2:=plot3d(K(30,30,x,y),x=-1..1,y=-1..1,color=brown):                                                                    

display([p1,p2]);
---------
However, when I execute the following code,  I get the error message "to many levels of recursion"
---------
restart;                                                                                                                

with(plots):                                                                                                          

 g:=(x,y)->sin(Pi*(x+y))*(x^2+y^2);                                                                  

 q:=(n,k,l,x,y)->binomial(n,k)*binomial(n-k,l)*(((1+x)/2)^k)*(((1+y)/2)^l)*(1-((1+x)/2)-((1+y)/2))^(n-k-l) ;                                              K:=(n,x,y)->(((1+n)*(2+n))/4)*sum(sum(q(n,k,l,x,y)*int(int(q(n,k,l,t,u)*g(t,u),u=-1..-t),t=-1..1),l=0..n-k),k=0..n);  p1:=plot3d(g(x,y),x=-1..1,y=-1..-x,color=blue):                                                                      

 p2:=plot3d(K(1,x,y),x=-1..1,y=-1..-x,color=brown):                                                                  

p3:=plot3d(K(2,x,y),x=-1..1,y=-1..-x,color=yellow):                                                                

p4:=plot3d(K(5,x,y),x=-1..1,y=-1..-x,color=green):                                                                    

p5:=plot3d(K(10,x,y),x=-1..1,y=-1..-x,color=red):                                                              

   display([p1,p2,p3,p4,p5]);
--------
Could you please help me with this problem. Thanks in advance.

Dear User!

Hoped you all are fine with everything. I am facing to determinte the integration of the following for n = 0 and for n>=1.

int(2*x^i*(x+n)^m*sqrt(-x^2+x), x = 0 .. 1)

I am unable to compute integral, it displays the function itself.

burrpdf := alpha*k*((x-gamma)/beta)^(alpha-1)/beta(1+((x-gamma)/beta)^alpha)^(k+1)

mean_burr_temp := simplify(x*burrpdf)

int(mean_burr_temp, x = gamma .. t)

Hello Everybody!
Please help me to find a way to write the Taylor's series of some function in factiorial or Gamma notation.
Please see the attached file and suggest me something.
taylor_series_general.mw

I've been using Maple 2018 only a few days now, was mostly using Maple 2016 and never had any issues with returning an output (at least one that wasnt my fault), but with 2018 I've seen a few times where a simple task would return an output of "__SELECTION" and then my input. No idea what this is or why its happening and all I really need to know is how to prevent it from happening. If its something with my preferences or settings that needs to be addressed, thats fine, but otherwise this is getting to be a real pain. See attached 

input -->

restart; with(plots);
H := 11;
B := x; W := x;
t__E := (13100*(B*B)*H*(.23-.10)*1.2)/(1500*alpha);
A__t := 2*B*W+2*H*(B+W);
OF := alpha/A__t;
for alpha from .1 by .1 to 2 do XX[alpha] := solve({0 < x, OF < 0.6951871658e-2, t__E < 200}, x) end do

result-->

         XX[0.1] := {0.3222041888 < x, x < 1.155224359}
         XX[0.2] := {0.6354894776 < x, x < 1.633733956}
         XX[0.3] := {0.9405579047 < x, x < 2.000907284}
         XX[0.4] := {1.238023973 < x, x < 2.310448718}
         XX[0.5] := {1.528429210 < x, x < 2.583160196}
         XX[0.6] := {1.812253750 < x, x < 2.829710218}
         XX[0.7] := {2.089925662 < x, x < 3.056436363}
         XX[0.8] := {2.361828525 < x, x < 3.267467912}
         XX[0.9] := {2.628307644 < x, x < 3.465673077}
         XX[1.0] := {2.889675191 < x, x < 3.653140182}
         XX[1.1] := {3.146214498 < x, x < 3.831445747}
         XX[1.2] := {3.398183646 < x, x < 4.001814567}
         XX[1.3] := {3.645818516 < x, x < 4.165220660}
         XX[1.4] := {3.889335368 < x, x < 4.322453755}
         XX[1.5] := {4.128933055 < x, x < 4.474164703}
         XX[1.6] := {4.364794925 < x, x < 4.620897435}
         XX[1.7] := {4.597090458 < x, x < 4.763112053}
         XX[1.8] := {4.825976698 < x, x < 4.901201868}
 

question -->

anyone knows a simple way how I can plot the points of the lower boundaries and upper boundaries of x as two line graphs (without copy pasting all the values into separate lists and then using the listplot command)?

thanks

I am working on a quantum mechanics problem and would like to get a 4x4 matrix A into diagonal form such that A=UDU^{-1}.  Basically I just need to know the values of D and U required to make A a diagonal matrix (where D is diagonal) as I can then use it to do an explicit calculation for a matrix exponential.  As it is the matrix is not diagonal, so I cannot use the explicit expression for the matrix exponential.  Is there a code with Maple that can calculate D and U simply?

The matrix is 4 x 4 and has elements 

1 0 0 1

0 -1 1 0

0 1 -1 0

1 0 0 1

I have a function involving sinh(x)/cosh(x) to evaluate (see attached SKS77.mw and S77.pdf). I got different values depending on whether or not the function is algebraically simplified. What's the right way to evaluate the exponential function in this case? Thanks

Occasionally I use the Variables palette to inspect some variables after a run. In Maple2018 it seems every Vector or Array returns something like "Empty variable structure" or similar. I never saw this in prior versions of Maple.

A bug? Or am I missing something??

M.D.

I have four spindle tori governed by the following equations:

I could plot the surfaces using implicitplot3d and I can imagine the volume common to these surfaces but I could not visualize it. So, am looking for a way to plot the volume covered by the surfaces such that f1<0, f2<0, f3<0 and f4<0. I know that it's easy in case of a 2D filled plot but is there any way this could be done for the 3D case? Any mathematical advice as to how to characterize or calculate this volume would also be great.

Why Maple does not simplify to 1

beta^(1/2)*(1+beta^(1/2))/(beta+beta^(1/2))

I'm trying to use the continued fractions expansion to simplify a fraction, and I need to cut the expansion off for large values (for example when a denominator is greater than 20). I have a list of the outputs but I'm struggling to find the correct commands to use in order to do this.

p := ContinuedFraction((q-1)/2^t);
print(p);
cf := Term(p, 0..100);
print(cf);
R := Convergent( p, 100);
r := denom(R);
printf("The order is %d"\n, r);
 

This is the section of code, any help would be appreciated, thanks.

Dear Users!

Hoped everyone fine with everything! I want to define a square matrix P whose elements are

p[i,j]=<φ[i],ψψ[j]>

printlevel := 2; for i from 0 while i <= 2^k-1 do for j from 0 while j <= M-1 do varphi[i, j] := t^j end do end do;
printlevel := 2; for i from 0 while i <= 2^k-1 do for j from 0 while j <= M-1 do phi[M*i+j+1] := varphi[i, j] end do end do;
printlevel := 2; for i from 0 while i <= 2^k-1 do for j from 0 while j <= M-1 do psi[i, j] := 2^((1/2)*k)*sqrt(2*j+1)*(sum((-1)^(j+i1)*factorial(j+i1)*(2*t-i)^i1/(factorial(j-i1)*factorial(i1)^2), i1 = 0 .. j)) end do end do;
printlevel := 2; for i from 0 while i <= 2^k-1 do for j from 0 while j <= M-1 do `&psi;&psi;`[M*i+j+1] := psi[i, j] end do end do;
 

take k=2,M=3