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Hello maple prime users

I have used the sequence command and series command in Maple before, but seem to have hit a little hurdle with a particular problem.

I want to run the expression:

h(a,b,c):=b!*(a+c)!*sum(F,n=0..c)

   Where F:=(-1)^n*binomial(c,n)*N(a+n):

   Where N(a):=(-1)^n*[evalf(ln(2)) - 1 + 0.5 -1/3 + 1/4 +... + (-1)^a/a]:

I ran a test case using the following code:

restart:
a:=1:
b:=2:
c:=3:
tot:=0:
F:=((-1)^(a+n)/(a+n)):

for n from 0 to c do
      Seq_F2:=(-1)^(a+n):
   
      Seq:=[seq(F,n=0..n)];
      Seq2:=convert(Seq, `+`);

      final:=Seq_F2*(evalf(ln(2))+Seq2);

      SS:=(-1)^n*binomial(c,n)*final;

      S:=(b!*(a+c)!)*SS;
      tot:=tot+S;
od:
tot;

This works for the case where a =1, but will not work for a>1 as in the N(a+n) sequence it misses out the terms in the series for a-1, a-2 etc.... So when a = 2 it misses out the -1 of the sequence and when a = 3 it misses out the -1 and 1/2. Are there any tips on how to overcome this?

 

Best regards

 

- Yeti

How do I check in maple if a series, is convergent or divergegent?

 

f:=((n-1)/2)/(1+((n-1)/2)^2);

 

is this function convergent or divergegent, and is it posible to decide only for odd n?

In Maple 2015, on windows 8.1 64-bit the command
series(2*x*(x-y)/y, y = 0, 3);
gives

which is incorrect. The answer is


You can notice the minus sign in front the the -2x is incorrectly typeset, which makes me wonder if it's a bug in the typsetting program and not series itself.

Please fix asap

plot.mw

 

Hi all. Please help me to plot this. I don't know why it doesn't work correctly.

Regards

prob1.mw    prob2.mw

Hi, I don't know why this happened...

If I write the command in new sheet, it runs correctly( prob2.mw).

 

Second, help me to evaluate N, please...  (prob1.mw)

 

Regards :-)

 

 

 

 

 

Hi

How can I obtain series expansion of a known mathematical function? for example I Need a command to get a formula for expansion of Bessel function as bellow

Hello,

i need help!!

write a procedure for the taylor series sin (x) and plot it in the range (-2pi to 2 pi)

use 20 term iterations in the taylor series approximation.

Thank you very much for your help.... 

I do not think the current API for dsolve when asking for series solution is done right. If one wants to obtain a series solution for an ODE, but wants different order than the default 6, now one must set this value using a global setting before making the call, like this:

eq:=diff(y(x),x$2)+y(x)=0;
Order:=10;
dsolve({eq,y(0)=1,D(y)(0)=0},y(x),type='series');

It would be better if options to calls are passed along with the other parameters in the call itself. Something like

dsolve({eq,y(0)=1,D(y)(0)=0},y(x),type='series',order=10);

This should also apply to any command that takes Order, such as series(cos(x),x=0,order=10);

Passing options and values to functions using global and environment variables is not safe and not a good way to go about it as it can cause programming errors.

Hi all!

F is a delta function:

F:=delta(x-x[0])*delta(y-y[0])

I want it be expaned through trigonometric series:

F:=sum(sum(Q[k*l]*sin(l*Pi*x/a)*sin(k*Pi*y/b), k = 1 .. infinity), l = 1 .. infinity)

So I want to get every Q:

Q[k, l] := `assuming`([4*(int(int(f[z1]*sin(l*Pi*x/a)*sin(k*Pi*y/b), x = 0 .. b), y = 0 .. a))/(a*b)], [k::posint, l::posint, a > 0, b > 0])

But it result in (when x[0]:=a/2, y[0]:=b/2):

4*(int(int(F[0]*exp(I*omega*t)*delta(x-x[0])*delta(y-y[0])*sin(l*Pi*x/a)*sin(k*Pi*y/b), x = 0 .. b), y = 0 .. a))/(a*b)

 

I wonder HOW CAN I GET THE EXACT RESULT:Q[k, l] := 4*sin(l*Pi/a)*sin(k*Pi/b)/(a*b)

THANKS!

Hi,

 

  Excuse me, I tried to substract in a series expansion. It works for Taylor-type expansion, but not Laurent-type ones

*********

ffff:=1/(t-3);
ggg:=taylor(ffff,t=infinity,3);
coeff(ggg,t,-1);


ffff:=exp(t);
ggg:=taylor(ffff,t=0,3);
coeff(ggg,t,1);

*********

Maple gives me


Error, unable to compute coeff


1

 

. My question is, why "coeff" does not work in the first case? how to make it work? Though I can copy the expansion part, assign it to another variable, and "coeff" will work

 

how to derive poincare series from symmetric function in maple

hi everyone , i need your point of view in my question,any help would be appreciated in advance .

we have a discrete function named g(t) and a continous function f(t) in in convolution integral just like this :
int(f(t-x)*g(x),x=0..t) ; 
we have just g(x) in some special points int the interval (0..t) , thus i need to convert this integral to a series.
how should i do this ? can anyone help or any idea ? i need at first a mathematical solution or idea about how to do this and then, how to do this in a software ?
tnx again.

Hello,

I am trying to figure out how to find several parital sums of the Airy's Function on a common screen. I figured out how to do it for a the Bessel fucntion of order 1, but I am not given the series for Airy's . Can anyone help me with what I would plug in to maple for the Airy's function or how I would go about finding the parital sums it would be greatly apperciated.

Thanks,

Rob

Does Maple have any tool or package that computes the Fourier & Fourier-Bessel series expansions of a given funtion "f(x)" over a specified interval "[a,b]"?

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