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These are questions asked by digerdiga

This is not a problem per se, but more to understand the background.


f := polylog(2, -x);

int(f/(x+1), x);

convert(f, dilog);

int(%/(x+1), x)


The integration of the polylog maple is not capable of doing, but after converting to dilog it finds an anti derivative.

That leads to the question, why is dilog as a separate to polylog(2,*) implemented anyway? Why couldn't it all be done with the more general polylog function?


I'm also wondering why maple has difficulties to integrate


for general a.


I have this error I'm not sure how to solve


`assuming`([simplify(int(ln(1+x)^3/(x+a), x = 0 .. 1))], [a > 0]);

combine(expand((eval(%, a = I)+eval(%, a = -I))*(1/2)))


What is the precise problem here?

Digits := 15;

b := -I;

a := sqrt(2);

epsilon := 1;

f := proc (t) options operator, arrow; evalf(Int(exp(I*k*t)/((1+a^2*sin(k)^2)*(k-b)^epsilon), k = -infinity .. infinity)) end proc;



I tried different methods like _d01amc, but either I have this error:

Error, (in evalf/int) NE_QUAD_NO_CONV:
  The integral is probably divergent or slowly convergent.

or it takes forever.

I also tried to map the interval to some finite length (k=tan(u)), but then I get

Error, (in evalf/int) NE_QUAD_BAD_SUBDIV:
  Extremely bad integrand behaviour occurs around the
  sub-interval (-1,5707963e+000, -1,5707963e+000 ).

disgusting integrand?


Digits := 32;

t0 := 1;

eq := 1-w*v^2-2*v*exp(-t/v);

equ := eval(eq, v = -t/ln(u));

us := solve(eval(equ, t = t0), u);

vs := -t0/ln(us);

plot(Re(vs), w = 0 .. 10, view = 0 .. 1)



I want to plot the solution of this equation, but it doesn't quite work. I tried to transform it, because I thought the singularity in the denominator of the exponential causes the issues.

any suggestions?


I'm wondering which connection formulas maple has access to?

For instance consider the following exmple


hypergeom([a, b], [c], 1);

`assuming`([convert(%, GAMMA)], [c-a-b > 0])


it should be simplified to GAMMA functions, but I do not get maple to do it. Are there packages for this?


Same for higher functions pFq for example

hypergeom([1, 1, 2*q-2+L], [2, L+1], 1)

under appropriate assumptions.

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