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

restart;

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

int(dilog(x+1)/(x+a),x)

for general a.

Hello,

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

restart;

`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?

restart;
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;

f(1.3)

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?

restart;

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?

Hello,

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

For instance consider the following exmple

restart;

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.