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

Let

f(x)= 2x^2 -2, x >= 0

Find d/dx f^-1(x)|(subscript x=0.)

Note that f(1)=0.

Use d/dx f^-1(x)= 1/(f'[f^-1(x)])

Hello

I was trying to introduce vector r_vec that has 3 components in x,y,z

I've attached my file, I've 2 questions here

first, why isn't the vector shown in as r_vec = () ei + () ej + () ek instead appears as a column vector

second, why doesn't it accept differentating

thank you
 

Download tst1.mwtst1.mw

I have the following pertubation problem I want to use maple to expand for me.

We have epsilon := eps;

x(t,eps):= x_{-1}(t)/eps+x_0(t)+x_1(t)*eps

z(t,eps):=z_{-1}(t)/eps+z_0(t)+z_1(t)*eps

I want to expand a Taylor series of the following function upto some arbitray order of eps, i.e O(eps^3) or higher (depending on my mood :-)), around t=0, f(x(t,eps),z(t,eps),cos(t/eps),sin(t/eps)).

Anyone has any suggestion how to use maple 2017.3 to do this?

Thanks!

c)Graph y=5x² and the tangent line at the point (-1,5) in the same coordinate system.

Manually, I was able to find the answer for (a). But how do I key in the Maple command for question (b) and (c) ?

Please help and thank you in advance.

My code.mw

Footnote: Can we use variation of parameters method in this question?