Items tagged with series

so yep pretty self explainatory, i was just wondering why it works when i use the asymptomatic expansion but not the iterated reciprocal substitution code shown in the that help interface for asympt.

``

``

Zeta(1/2+I*y)

Zeta(1/2+I*y)

(1)

subs(y = 1/y, series(subs(y = 1/y, Zeta(1/2+I*y)), y = 0, 6))

Error, (in series/Zeta) unable to compute series

 

asympt(Zeta(1/2+I*y), y, 6)

1+exp(-I*ln(2)*y)+exp(-I*ln(3)*y)+exp(-(2*I)*ln(2)*y)

(2)

``


 

Download MAPLE_IS_FUNNY.mw

Download Sum_Sum.mw
 

Restart:

Digits := 10:

Ha := 2:

R := 2:

a := 0.1e-2:

Rt := 1:

Br := 1.5:

Xi := 0:

U[0] := 0:

U[1] := alpha:

U[2] := -6+(1/16)*Rt*Xi:

U[3] := (1/6)*beta:

T[0] := -(1/2)*Rt:

T[1] := phi:

``

delta := proc (k) options operator, arrow; `if`(k = 0, 1, 0) end proc;

proc (k) options operator, arrow; `if`(k = 0, 1, 0) end proc

(1)

for k from 0 to 10 do U[k+4] := ((Ha^2+R)*U[k+2]+Xi*T[k+2])/((4*(k+3))*(k+4)); sum((1+(4/3)*R+4*a*R*T[i])*(k-i+1)*(k-i+2)*T[k-i+2], i = 0 .. k) := -4*a*R*(sum((i+1)*T[i+1]*(k-i+1)*T[k-i+1], i = 0 .. k))-Br*(sum((i+1)*U[i+1]*(k-i+1)*U[k-i+1], i = 0 .. k))+(1/4)*Ha^2*Br*(sum(U[i]*U[k-i], i = 0 .. k)) end do:

u := sum(U[j]*y^j, j = 0 .. 9)

alpha*y-6*y^2+(1/6)*beta*y^3-(3/4)*y^4+(1/80)*beta*y^5-(3/80)*y^6+(1/2240)*beta*y^7-(9/8960)*y^8+(1/107520)*beta*y^9

(2)

``


 

Download Sum_Sum.mw

 

I am dealing relatively often with vector functions of a variable vector. Specifically these are (in general nonlinear) mappings from R^6 to R^6, and often I have one or more extra parameter that controls the map.

Often I'd like to get a first-order expansion of these. The general scheme I use to do that is to map mtaylor over the components of the function vector. Like so:

map(mtaylor,F(<x1...x6>),[x1...x6,p1...pn],order);# F(<...>)  is  <F1(<..>)..F6(<...>)>

This works fine until I hit a situation where the Taylor expansion for one of the parameters p does not exist. Then it bombs. Actually, I often can use assumptions on the parameters to prevent bombing; however, in that case I often get the unchanged function F returned. This is Bad as the whole thing happens in a loop with many concatenated functions F, and now expression swell makes Maple lock up.

In at least a significant subset of these functions, the series command works where taylor fails. "mseries", however, does not exist in Maple. So my question is whether someone has written an "mseries" command for Maple. I know how to do it in principle (but caution is needed to make it work as intended), however, I wonder whether either someone has done it before and might share his/her code, or whether there is a reason why "mseries" actually cannot work.

TIA,

Mac Dude

 

how to solve  Fourier Series on maple ??

how to find the first 6 non-zero terms of MacLaurin series of the function erf(x)

Hi all, 
I was only wondering if there is a way how to trunk a solution using a maple command.

I want to use it to give a truncation error which is equal to :(14/45)(D^5)(y)(0) h^5

The result I am getting is as followed: (it is correct, I just want to cut off the bit with the power of 6)
........
......
>error:=expand(Yx[i+1]-Yx[i-3]-(4*h/3)*(2*f[i-2]-f[i-1]+2*f[i]));
                          
          error :=  (14/45)(D^5)(y)(0) h^5  + 7/10 (D^6)(y)(0) h^6
                  
thank you in advance

Find the first 6 non-zero terms of MacLaurin series of the function erf(x)

I have computed the eigenfunction expansion for f(x)=x on 0<x<1 in terms of the eigenfunctions exp(-x/2)*sin(n*Pi*x).

I wish to calculate the weighted L2 error in this expansion (the weight function is w(x)=exp(x)).

Specifically, I want to determine how many terms in the eigenfunction expansion are necessary for the error to be less than say 0.3.

Here is the code:

f := x -> x
w := x -> exp(x)
assume('n', integer);
y :=  (n, x) -> exp(-x/2) sin(n Pi x)       
c := n-> (int(f(x)*y(n, x)*w(x), x = 0 .. 1))/(int(y(n, x)^2*w(x), x = 0 .. 1))
Fourierf := (n, x) -> sum(c(j)*y(j, x), j = 1 .. n)

fsolve(Lerror(n) = 0.3, n);

This seems to run forever without giving a value of n.  I know this is a large computation, but it seems that Maple should be able to handle it.  Does anyone have any suggestions?

Heather

 

f=sum((2*q*cos(2* i*x)*(-1)^(i)*(-1)^((2*i-1)))/(i*Pi),i=1.3.5...35)

I want to write this series but getting error

the result is

2*q*cos(2*x)/Pi-2*cos(6*x)*q/(3*Pi)+2*q*cos(10*x)/(5*Pi)-2*q*cos(14*x)/(7*Pi)+2*q*cos(18*x)/(9*Pi)-2*q*cos(22*x)/(11*Pi)+2*q*cos(26*x)/(13*Pi)-2*q*cos(30*x)/(15*Pi)+2*q*cos(34*x)/(17*Pi)-2*q*cos(38*x)/(19*Pi)+2*q*cos(42*x)/(21*Pi)-2*q*cos(46*x)/(23*Pi)+2*q*cos(50*x)/(25*Pi)-2*q*cos(54*x)/(27*Pi)+2*q*cos(58*x)/(29*Pi)-2*q*cos(62*x)/(31*Pi)+2*q*cos(66*x)/(33*Pi)-2*q*cos(70*x)/(35*Pi)

can anybody help 

Hey all,

my goal is to get a taylor expansion in Maple up to n-th order of a function y(t) (not defined in more detail, just abstract).

I want to taylor this function around tn, and I want the series for tn+1=tn + h. I would expect to get (as an example: 4th order)

y(tn+1) ≈ y(tn) + h* y'(tn) + h2/2*y''(tn) + h3/6*y'''(tn) + O(h4).

My command was:

and I get:

Can someone maybe point out what I am doing wrong and how I can fix it?

Thanks in advance!

Tim

Dear Community,

I have two measured series - time series actually, stored in Excel:

  • gas flow (ordered in ascending date order),
  • pressure measurements (unordered, more or less randomly distributed dates),

I would like to:

  • import the two series into Maple,
  • convert them to time series,
  • merge them in a way, that the unordered pressure dates are plugged into the ordered gas flow dates, so I finally get a single, ordered date sequence of ascending order.
  • pressure and gas flow rates should remain separated of course, i.e. not merged (they should appear in two separate vectors, or matrix columns, whatever)
  • if pressure dates and gas flow dates are the same, they should naturally be in the same row, i.e. belong to the same date.

No problems with the import, but I'm lost with the time series handling. I tried to figure it out from the help, but frankly the description is rather difficult, and I also haven't found appropriate examples. Is it possible to do it with Maple's time series feature at all, or something other is more practical? Files and my initial trial are attached.

tx in advance

best regards

Andras

Time_Series_Data.xlsx

TimeSeriesTest.mw

Hi! I'm trying to find the way to plot the solution with series representation. I need some help to find the easiest way.

Note: I realized some typing errors, which do not change the question a lot ,and I corrected them.

plot.mw

I wish to study the trend of medical consultations each day during six years. Thus I expect near 2200 datas to analyse.

But some parameters are to consider :

- I don't have yet the datas per day, but the mean is about 2 consultations per day

- as it is difficult to do more than 3 or perhaps 4 consultations during one day (9h30 am - 13h pm), the others if they exist will probably be seen the next day (aso if the next day 3 news consultations occured)

- then, I don't know actually (as I expect the datas or each day but don't have now these datas) if the better distribution will be simply follow a Poisson' law, or exponential, or negative binomial, ..

- do someone have a clue for the better law given what i said ?

 

Further, I don't have a stastic program especially used for time trend, excepting Systran 13, but I don't believe that this program can be used with a theoric model of distribution, I recall that it does usual tasks, autocorrelations, saisonnal adjustments, .. but with continuous distributions I believe, and a linear model (removing the basic frequencies)

As such program (study of temporal series) is usually sold about 3000$ in France, that I don't expect to be a trader, with only one calculus to do, could anyone tell me how to adjust the better model to the 2200 datas that could be expected ?

Thx for your help, friendly yours;

Milos

Dear all

I have a simple question about geometric series

What's the difference between g(2) and gg(2)

 Many thanks

 

 

Geometric_series.mw

 

Dear all

 

If its possible in  Maple to change the integral of the sum to  the sum of integrals when I calucle the integral of a function series

 

Thank you

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