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.

Hello,
I want to collect a function into terms without using ?expand() since this expands everything which I dont want.

f:=GAMMA(L+2*q-3-k)/(GAMMA(L-k)*k)*((GAMMA(-2*q+L)*GAMMA(L+2*q-3-k)-GAMMA(L+2*q-3)*GAMMA(L-2*q-1-k)*(L+2*k-1-(4*k+2)*q))/((2*(-1+2*q))*(4*q-3)*GAMMA(L+2*q-3)*GAMMA(L+2*q-3-k)));
collect(f,[k,GAMMA])

then has 1 term which still contains a denominator, but I want them seperate so I can use ?op() for all additive terms.

Is there an option without expanding the entire thing to enforce termwise selection?

Of course I could do it in a second step, but I want to avoid it and think it should be simpler.

This is a follow up question to https://mapleprimes.com/questions/225877-Partial-Integration-Hint:

restart;

with(Physics, KroneckerDelta);

Digits := 15;

t4 := 1/3;

n := 4;

q := 4/7;

i1 := evalf(Int(t^n*exp(-t)*GAMMA(2*q-2, t*(1-t4)*(1/t4)), t = 0 .. infinity, method = _d01amc));

i2 := expand(simplify(GAMMA(2*q-2)*add(binomial(n, m)*(KroneckerDelta[m, 0]-GAMMA(3-2*q)*(1/GAMMA(3-2*q-m))*t4^m*(1-t4)^(2*q-2))*(-1)^m*factorial(n-m), m = 0 .. n)));

`~`[evalf]([op(i2)]);

add(%);

i3 := expand(simplify(eval((-1)^n*GAMMA(2*q-2)*(diff((1-(1+t4*x*(1/(1-t4)))^(2-2*q))*(1/x), x$n)), x = 1)));

`~`[evalf]([op(i3)]);

add(%)

Interestingly this works up to n=3. It seems that the second term is wrongly manipulated and it should be 168/6 instead of 175/6?

I doubt the derivatives are wrong since I checked individually. I also hardly doubt this is a numerical round off, as the discrepancy is too large.

Is this a bug, or is there actually an error?