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Hi,

I open a discussion about convolution and Fourier coefficients in Fourier series.

 

I have a function defined by f(x)=0 if x in [-Pi,0[ and 1 if x in [0,Pi[, of course f 2*Pi periodic function.

My goal is compare the Fourier coefficients of f*f ( * convolution ) and The Fourier Coefficient of f.

 

Thanks for your help.

 

 

 

Find serie cosine Nice question...

Yesterday at 3:50 PM sarra 105

Hi,

Maybe a good question.

Write  f(x)=ln(abs(cos(x)))   with infinite serie cosine(2*n*x).

Thank for your remark.

 

 

Hello,

I have this expression on image below and I would like to do multi taylor in these variables. The maple says that the expansion is not possible to do. Does somebody know where the problem could be ? Thank you very much for help.

Equation:

Taylor series:

 

 

how maple calculate exp(x) with e.g. 100000 decimal numbers

a divsion of the series x^k/k! with e.g. 1/25000!/25001 lasts longer than the exp(1.xx) calculation

 

is there a faster way to calculate exp(x) than with the x^k/k! series

 

thanks

 

 

 

 

 

 

 

 

Dear All;

Happy, to discuss with you these lines, and thank you to help me.

My goal is:

 

ode := D(y)(x) = f(x,y(x));
                          
In this expression, is assumed to be a known function of the independant variable
                                      x
 and the function that we are trying to solve for
                                    y(x)
.  The simplest numerical stencils to solve this equation will give us an approximation to
                                      y
 at some point
                                  x = X + h
 given some knowledge of
                                      y
 at
                                    x = X
.  All of these stencils are based on the Taylor series approximation for
                                    y(x)
 about
                                    x = X
 to linear order:
eq1 := y(x) = series(y(x),x=X,3);
                       
eq2 := h = x - X;
eq3 := subs(isolate(eq2,x),eq1);
                                
Now, we can remove the first derivative of y
                                     
 by making use of the differential equation:
eq4 := subs(x=X,ode);
eq5 := subs(eq4,eq3);
                           

Now we must compute the same for y(x-h)  and then make.  How can I do this please

Simple question...

February 27 2014 sarra 105

Dear All,

I have a simple question I try to find the Fourrier Series of:

 f(x)=x*e^{I*x}

with maple or without maple.

Thanks

 

 

Dear all;

Special thanks for all the member who help me in Maple.

My last question is:

Write a maple procedure that solves for y(1) in the initial value problem y'(x)=f(y), y(0)=1

using a Numerical stencil based on the n^{th] order taylor series expansion of y.

The procedure arguments include an arbitrary function f, an integrer n, representing the accuracy of the taylor series expansion, and N representing the number of steps between x=0 and x=1.

 

 

 

Is there a simple way, given a functional equation satisfied by a formal power series, to obtain the explicit form (the Taylor expansion) of this formal power series? For example, my input is "f(x)=1+x*f2(x)", and I want to have as the output: "1+x+2x2+5x3+O(x4)".

Many thanks!

I'm attempting to plot several solutions of this differential equation (I have uploaded my worksheet). I have used this series of commands before without issue, but for some reason I keep getting the error message: "Error, (in plot) incorrect first argument" ect.. Does anyone have any insight into what might be going wrong? Thank you.

Download ass_1_#9.mw

ass_1_#9.mw

Hi, i need help. I'm currently working with Taylor and Maclaurin series in Maple. I can easily compute the sum by typing in fx : 

taylor( (ex,x=0, 5) , and then I get the first 5 numbers of the series. But I would like Maple to write the series as a sum from n =0 to infinity fx.  I can't figure out how to do it. Can it be done? 

Thanks for helping.

M5 :=series((1+1/(2*a^2)+(1/2)*b^2-1/(2*a))^a, a=0,3);

there is a variable b too

Can anyone help me to transform a system of ODE into a power series solution. The system of ODE is as follows:

diff(f(eta), eta, eta, eta)+(diff(f(eta), eta, eta))*f(eta)+1 - (diff(f(eta), eta))^2=0

f(eta)*(diff(theta(eta), eta))+(1/Pr)*diff(theta(eta), eta, eta)=0

where Pr is the prendtl no.

I have following expression:

y1:=t->1/(4*cosh(t)^2)

I:=int(y1(t)^2,t=-T/2..T/2)

Now I tried:

MultiSeries:-asympt(I,T,5)

for which I only get the highest order.

Can I increase the order in any way?

Is there a way to tell Maple to expand a complex function in Laurent series around a point, and have it show the series expansion that are valid for different regions? Either by the user telling it which region to use, or it automatically shows all regions?

For example, given

f(z):= z-> (3*z+1)/((z-1)*(z+1))

This has a pole at z=1 and at z=-1. I want to expand this around z=1. Hence it will have Laurent series in the annulus between z=1 and z=-1, but there is also region outside z=-1 that goes to infinity. So there are two regions.

When I do

with(numapprox);
laurent((3*z+1)/(z^2-1),z=1);

Maple gives the correct Laurent series for the region in the annulus |Z-1|<2, i.e. the first region (the one inside the two singularities).

But I want to see the expansion for different region, for |z-1|>2 (to check if I did it ok). This is what I get btw

3/(z-1) - 2/(z-1)^2 + 4/(z-1)^3 - 8/(z-1)^4 +.... 

Do I need a special package for this?

Fyi, I found this question here but it does not really answer my question. I want to speficy both the point of expansion, and also the region itself.

 

 

Here is a screen of the original question  http://www.mapleprimes.com/ViewTemp.ashx?f=21095_1385385286/screen25.11.13.docx

 My advice to the questioner is to visit a psychiatrist ASAP.

Markiyan Hirnyk

 

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