Mariusz Iwaniuk

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These are questions asked by Mariusz Iwaniuk

In Maple 2018 help written:

The interpolation methods available in the Interpolation package all work as follows. First, the user calls one of the commands in the package, submitting the input points and the values at these points. This returns an object encapsulating all the data and options submitted. This object can then be used like a normal mathematical function, e.g. for plotting, integration, or just to evaluate at a given point.

The Interpolation[Interpolate] command was introduced in Maple 2018
 

My test example:

with(Interpolation):

points := [seq(x, x = 0 .. 10, 1)]; data := [seq(sqrt(1.+x^2), x = 0 .. 10, 1)];

f := Interpolate(points, data);

f(1); # OK works :).

int(f(x), x = 0 .. 1); # Not working ?

int(f(x), x = 0 .. 1,numeric); # Not working ?

eval(diff(f(x), x), x = 2);# Not working ?

plot(f(x), x = 0 .. 10);#  OK works :)

plot([f(x), diff(f(x), x)], x = 0 .. 10);# Not working ?

plot([f, diff(f, x)], 0 .. 10);# Only a half  working ?

 

Thanks.


 

 

I have PDE i trying to solve the equation using series.

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) = Pi, series, order = 2);

Give me: "Error, (in DifferentialAlgebra:-RosenfeldGroebner) unexpected occurrence of the non-rational constants {Pi} in the given input" ?

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) =gamma, series, order = 2);#gamma = 0.5772156649,Gives ERROR ?

If I  change instead of Pi is e or exp(1) works fine.

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) = exp(1), series, order = 2);#OK.

 

It's a bug, design or  something else ?

 

int(exp(-sec(t))*cos(t)/(-1/4+sin(t)^2), t = 0 .. (1/2)*Pi, CauchyPrincipalValue = true, numeric = true);

Returns unevaluated for me.

I tried all the methods in HELP documentation and I failed.
Integral is singular at point 1/4.

Thank you.

I have a expression with polylog functions.I want to simplifying to Pi's constans.I tired with:

1. simplify
2. convert

but seems dosen't work:

simplify(sum((sin(k)/k)^7, k = 0 .. infinity))

#1+(1/128*I)*polylog(7, exp(7*I))-(7/128*I)*polylog(7, exp(5*I))+(21/128*I)*polylog(7, exp(3*I))-
(35/128*I)*polylog(7, exp(I))+(35/128*I)*polylog(7, exp(-I))-(21/128*I)*polylog(7, exp(-3*I))+
(7/128*I)*polylog(7, exp(-5*I))-(1/128*I)*polylog(7, exp(-7*I))

 Mathematica give me:

How to do it in Maple?

Hi Dears,

I'm have a code like this:

sum(-GAMMA(k+1, x), k = 0 .. -2) and Maple give me : Ei(1, x).

How to check that answer is correct?

 

Thank you in advance.

I am looking forward to hearing from you.

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