This question is related to the recent post
http://www.mapleprimes.com/questions/211460-Series-Of-Bessel-Functions

1. Consider the following fast convergent series:

f:=n->(-1)^(n+1)*1/(n+exp(n));
S1:=Sum(f(n),n=1..infinity);
evalf(S1);
S2:=Sum(f(2*n-1)+f(2*n),n=1..infinity);
evalf(S2);

As expected, the sum of the series is obtained very fast (with any precision), same results for S1 and S2.


2. Now change the series to a very slowly convergent one:

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

evalf(S1) is computed also extremely fast, because the acceleration algorithm works here perfectly.
But evalf(S2) demonstrates a bug:

Error, (in evalf/Sum1) invalid input: `evalf/Sum/infinite` expects its 2nd argument, ix, to be of type name, but received ...


3. Let us take another series:

f:=n->(-1)^(n+1)/sqrt(n+sqrt(n)*sin(n));

Now evalf(S1) does not evaluate numerically and evalf(S2) ==> same error.
Note that I do not know whether this series is convergent or not, but the same thing happens for the obviously convergent series

f:=n->(-1)^(n+1)/sqrt(n^(11/5)+n^2*sin(n));

(because it converges slowly (but absolutely) and the acceleration fails).
I would be interested to know a method to approximate (in Maple) the sum of such series.

Edit. Now I know that the mentioned series 

converges (but note that Leibniz' test cannot be used).

I am trying to have the output of DETOOLS as 3dpolarplot. As in the following example:

EF := {2*(diff(w[2](t), t)) = 10, diff(w[1](t), t) = sqrt(2/w[1](t)), diff(w[3](t), t) = 0}; with(DEtools); DEplot3d(EF, {w[1](t), w[2](t), w[3](t)}, t = 0 .. 100, [[w[1](0) = 1, w[2](0) = 0, w[3](0) = 0]], scene = [w[1](t), w[2](t), w[3](t)], stepsize = .1, orientation = [139, -106])

how can I get the output as a polarplot in 3d where, w[2] and w[3] have range 0..2*pi.

Please help in this respect asap.

Hello,

I would like to obtain the display of several outputs from a procedure.

Sorry for this question which should be quiet simple but I didn't manage to solve my issue. By the past, I always wanted to obtain only one output from a procedure.

I put attached a example of procedure which calculates x^2 and x^3 for a given value of x.

With my procedure, I didn't obtain the display of the output calculating the square value.

How can I display all the outputs of a procedure ?

Thank you for your help

ExampleOfprocedure.mw

As a college project we have to implement the caesar cipher on maple but as beginners we haven't got a clue. 

Any advice even on how to begin please?

I am using maple 13 to found Eingenvalues of an hermitian matrix :

M1:=Matrix([
> [lambda3+lambda4,0,0,0,0,0,lambda4/sqrt(2),0,0,I*lambda4/sqrt(2)],
> [0,lambda3/4,0,0,0,0,0,0,0,0],
> [0,0,lambda3/4,0,0,0,0,0,0,0],
> [0,0,0,lambda3/4,0,0,0,0,0,0],
> [0,0,0,0,lambda3/4,0,0,0,0,0],
> [0,0,0,0,0,lambda3,0,0,0,0],
> [lambda4/sqrt(2),0,0,0,0,0,lambda3/2,0,0,0],
> [0,0,0,0,0,0,0,lambda2,0,0],
> [0,0,0,0,0,0,0,0,lambda2,0],
> [-I*lambda4/sqrt(2),0,0,0,0,0,0,0,0,lambda4/2]
> ]);

>Eigenvalues(M1);

my surprise is that maple gives me 8 correct solutions an 2 complex eigenvalues which are not acceptable (we now that the eigenvalues for an hermitian matrix are all real) .

To understand the output of maple, first,  I suspect that the complex part of the roots was null but without success I haven't found how to do it zero...

is it a bug? Thanks a lot to cooperation

Hello,

I have .mla. package and I would like to create the source code associated to this package.

In the past, you have also help me to obtain the source code of procedure of the module.

Here the post where Carl Love has helped me :

http://www.mapleprimes.com/questions/203676-Open-A-Maple-Package

How can I do to create the complete source code of package directly ?

Is there a direct way enabling to not have to read one procedure by one procedure but to obtain the code source for all the package ?

Thank you for your help

Environment: Maple2015, MATLAB_R2014b(MacOSX10.8.5), 2015b(MacOSX10.11.4)

MapleToolbox2015.1MacInstaller.app was successfully completed (log tells us), but when MATLAB were booted, following error messages appeared and symbolic operations of maple failed. 

This would be closely related to maple installation on MATLAB as such errors never occur for clean install of MATLABs and looks independent on OSX versions. Now javaforosx.dmg in use by instruction of Maplesoft.  Something wrong is in Maple2015. Note maple-MATLAB link works normally.

Please provide us with direction of how to fix it hopefully by Maplesoft professionals.

(Quote of MATLAB command window display)

Exception in thread "Startup Class Loader" java.lang.UnsatisfiedLinkError: jogamp.common.os.MachineDescriptionRuntime.getPointerSizeInBytesImpl()I

at jogamp.common.os.MachineDescriptionRuntime.getPointerSizeInBytesImpl(Native Method)

at jogamp.common.os.MachineDescriptionRuntime.getRuntimeImpl(MachineDescriptionRuntime.java:138)

at jogamp.common.os.MachineDescriptionRuntime.getRuntime(MachineDescriptionRuntime.java:124)

at com.jogamp.common.os.Platform.<clinit>(Platform.java:228)

at javax.media.opengl.GLProfile.<clinit>(GLProfile.java:83)

at com.mathworks.hg.peer.JavaSceneServerPeer.initializeJOGL(JavaSceneServerPeer.java:114)

at com.mathworks.hg.peer.JavaSceneServerPeer.<clinit>(JavaSceneServerPeer.java:100)

at java.lang.Class.forName0(Native Method)

at java.lang.Class.forName(Class.java:190)

at com.mathworks.mde.desk.StartupClassLoader.loadClass(StartupClassLoader.java:258)

at com.mathworks.mde.desk.StartupClassLoader.access$900(StartupClassLoader.java:25)

at com.mathworks.mde.desk.StartupClassLoader$2.run(StartupClassLoader.java:244)

at java.lang.Thread.run(Thread.java:745)

>> maple();

error: maple (line 178)

Invalid MEX-file '/Applications/MATLAB_R2014b.app/toolbox/maple/maplemex.mexmaci64':

dlopen(/Applications/MATLAB_R2014b.app/toolbox/maple/maplemex.mexmaci64, 6): Symbol not found: ___sincos_stret

  Referenced from: /Library/Frameworks/Maple.framework/Versions/2015/bin.APPLE_UNIVERSAL_OSX/libhf.dylib

  Expected in: /usr/lib/libSystem.B.dylib

 in /Library/Frameworks/Maple.framework/Versions/2015/bin.APPLE_UNIVERSAL_OSX/libhf.dylib

>> syms x  y

error: sym (line 186)

Invalid MEX-file '/Applications/MATLAB_R2014b.app/toolbox/maple/maplemex.mexmaci64':

dlopen(/Applications/MATLAB_R2014b.app/toolbox/maple/maplemex.mexmaci64, 6): Symbol not found: ___sincos_stret

  Referenced from: /Library/Frameworks/Maple.framework/Versions/2015/bin.APPLE_UNIVERSAL_OSX/libhf.dylib

  Expected in: /usr/lib/libSystem.B.dylib

 in /Library/Frameworks/Maple.framework/Versions/2015/bin.APPLE_UNIVERSAL_OSX/libhf.dylib

 error: sym (line 56)

           assignin('caller',varargin{i},sym(varargin{i})); 

(Unquote)

How i need to write 

>teksbiasa:=`Hello! Bob`;

in button Action When Clicked at simple graphical interface instead of

Do(teksbiasa=%txtTeksBiasa);

because when i enter Hello! Bob in %txtTeksBiasa, system pop up ERROR

Error

Error in Component button with caption "Botton":

(in unknown) incorrect syntax in parse: missing operator or

`;`(near 7th character of parsed string)

Thank you~=]]

I'm having trouble evaluating an expression with an infinite sum of bessel functions. The expression is:

or, in mathematical notation:

The program doesn't seem to be able to solve the expression and return a value. I only get the answer

When I try to evaluate a simple infinite sum like 

the answer is a value. Breaking up the expression in components and evaluating each one works in some cases, e.g. the expression 

which returns a value. However, the expression

fails, and returns

Is there a trick to evaluating infinite sums with indices appearing inside a function in the summation expression? Or am I doing something wrong?

For example:

[2,4,9,15,20]

I want the output be 2491520.

Any command can solve the problem? Thank you.

>message:=`67A`;

67A

>P:=convert(message, bytes);

[54, 55, 65]

>with(Bits):

>bitP1:=Split(P1);

[0, 1, 1, 0, 1, 1]

>bitP2:=Split(P2);

[1, 1, 1, 0, 1, 1]

>bitP3:=Split(P3);

[1, 0, 0, 0, 0, 0, 1]

>with(Statistics):

>b1:=Count(bitP1);

6

>b2:=Count(bitP2);

6

>b3:=Count(bitP3);

7

>totalBits=b1+b2+b3;

19

Hi, how i need to modify my command so when i write any message with any lenght, i can get the totalBits directly..

Thank you~=]]

Hello..  I want to know if there is anny command to show the matrix of linear system.  I recently entred a 64 equations and i solved it by command solve,  but i want to show the matrix of system..  So plz. Help 

Sorry for boring you my friends. I am haunted by a problem of how to omit the undesired term.

For example, in the following equation, the a(t) , b(t), c(t), u(t), v(t), w(t), psi(t), phi(t), theta(t), varsigma(t), tau(t) and upsilon(t) and their first and second direvative to time t are considered as first order small variables. How could I omit the term greater than second order of small variables?

If we omit the undesired by hand, the omitted equation takes the form of:

R^2*rho*h*(diff(w(t), t, t))*Pi+R^2*rho*h*(diff(c(t), t, t))*Pi = 0;

The original equation is given as: 

-R^2*rho*h*cos(Omega*t)*(diff(tau(t), t, t))*a(t)*Pi+tau(t)*R^2*rho*h*(diff(tau(t), t))^2*a(t)*cos(Omega*t)*Pi-tau(t)*R^2*rho*h*(diff(tau(t), t))^2*b(t)*sin(Omega*t)*Pi+tau(t)*a(t)*Pi*cos(Omega*t)*(diff(varsigma(t), t))^2*R^2*h*rho+tau(t)*R^2*rho*h*a(t)*Omega^2*cos(Omega*t)*Pi-tau(t)*sin(Omega*t)*Pi*(diff(varsigma(t), t))^2*b(t)*R^2*h*rho-tau(t)*R^2*rho*h*b(t)*Omega^2*sin(Omega*t)*Pi+2*tau(t)*R^2*rho*h*(diff(a(t), t))*Omega*sin(Omega*t)*Pi+2*tau(t)*R^2*rho*h*(diff(b(t), t))*Omega*cos(Omega*t)*Pi-varsigma(t)*a(t)*sin(Omega*t)*Pi*(diff(varsigma(t), t))^2*R^2*h*rho-varsigma(t)*a(t)*sin(Omega*t)*Pi*Omega^2*R^2*h*rho-varsigma(t)*Pi*cos(Omega*t)*(diff(varsigma(t), t))^2*b(t)*R^2*h*rho-varsigma(t)*Pi*cos(Omega*t)*b(t)*Omega^2*R^2*h*rho-2*varsigma(t)*sin(Omega*t)*Pi*(diff(b(t), t))*Omega*R^2*h*rho+2*varsigma(t)*Pi*cos(Omega*t)*(diff(a(t), t))*Omega*R^2*h*rho+2*a(t)*Pi*cos(Omega*t)*(diff(varsigma(t), t))*Omega*R^2*h*rho-2*sin(Omega*t)*Pi*(diff(varsigma(t), t))*b(t)*Omega*R^2*h*rho+R^2*rho*h*(diff(tau(t), t, t))*sin(Omega*t)*b(t)*Pi+R^2*rho*h*(diff(w(t), t, t))*Pi+R^2*rho*h*(diff(c(t), t, t))*Pi-R^2*rho*h*(diff(tau(t), t))^2*c(t)*Pi+2*varsigma(t)*(diff(tau(t), t))*a(t)*Pi*cos(Omega*t)*(diff(varsigma(t), t))*R^2*h*rho-2*varsigma(t)*(diff(tau(t), t))*sin(Omega*t)*Pi*(diff(varsigma(t), t))*b(t)*R^2*h*rho+a(t)*sin(Omega*t)*Pi*(diff(varsigma(t), t, t))*R^2*h*rho+Pi*cos(Omega*t)*b(t)*(diff(varsigma(t), t, t))*R^2*h*rho-varsigma(t)*Pi*c(t)*(diff(varsigma(t), t, t))*R^2*h*rho-2*tau(t)*R^2*rho*h*(diff(tau(t), t))*(diff(c(t), t))*Pi-2*varsigma(t)*Pi*(diff(varsigma(t), t))*(diff(c(t), t))*R^2*h*rho+2*sin(Omega*t)*Pi*(diff(varsigma(t), t))*(diff(a(t), t))*R^2*h*rho+2*Pi*cos(Omega*t)*(diff(varsigma(t), t))*(diff(b(t), t))*R^2*h*rho-Pi*(diff(varsigma(t), t))^2*c(t)*R^2*h*rho-2*R^2*rho*h*cos(Omega*t)*(diff(tau(t), t))*(diff(a(t), t))*Pi+2*R^2*rho*h*(diff(tau(t), t))*sin(Omega*t)*(diff(b(t), t))*Pi+tau(t)*R^2*rho*h*(diff(b(t), t, t))*sin(Omega*t)*Pi-tau(t)*R^2*rho*h*(diff(a(t), t, t))*cos(Omega*t)*Pi-tau(t)*R^2*rho*h*(diff(tau(t), t, t))*c(t)*Pi+2*R^2*rho*h*Omega*sin(Omega*t)*(diff(tau(t), t))*a(t)*Pi+2*R^2*rho*h*(diff(tau(t), t))*Omega*cos(Omega*t)*b(t)*Pi+varsigma(t)*sin(Omega*t)*Pi*(diff(a(t), t, t))*R^2*h*rho+varsigma(t)*Pi*cos(Omega*t)*(diff(b(t), t, t))*R^2*h*rho = 0;

Thank you in advance for taking a look ;)

Suppose that I have a plot:

plot(sin((1/180)*Pi*x), x = -180 .. 180)

I want to add a degree symbol after the tickmarks on the x-axis.  One approach which seem promising is to add a plot option for the x-axis:

axis[1] = [tickmarks = [90 = typeset("90", degree)]]

where "degree" is replaced by a code for the degree symbol. Maple is helpful here because I can point and click using the Common Symbols palette and insert a degree symbol. However this does not work delivering an error "Error, invalid neutral operator". This error is undocumented. 

I can insert a Pi or an infinity symbol. If I want to I can put a degree sysmbol into ther title, but apparently not on the axes.

I've got the following:

Integral_over_region.mw

M_Iwaniuk