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These are questions asked by digerdiga

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.

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


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:


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)));



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)));




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?

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