J F Ogilvie

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17 years, 351 days

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These are questions asked by J F Ogilvie

int( exp(-2*r)*cos(theta)^3*r^2*sin(theta), phi=0..2*Pi, theta=0..Pi, r=0..infinity);
                      undefined

This integral with cos(theta) to an odd power should evaluate to zero, as found in Maple 17 [moderator: and up to Maple 2015.2] but not the most recent versions.

sum( (-1)^k/k * sin(k*x), k=-infinity..infinity);

  (mathematica solves this instantly.)

     I asked a similar question a few weeks ago and received a most helpful response, but unfortunately I had inaccurately transcribed thespecified form of that double integral from a file presented in Microsoft Word.  I shall be most grateful for the numerical evaluation of this difficult double integral here presented in unambiguous and correct Maple definition, for cases n=0 and n=1.

 

i1 := Int(exp(-(k^2*sinh(s)^2/(gam-I*k*cosh(s)) + I*k*(1-cosh(s)))*v)*Hypergeom([I/k],[1],I*k*v)*v^n, v=0..R/2);

Jn := 1/R*Int(sinh(s)*coth(s/2)^(2*I/k)/(gam-I*k*cosh(s))^5*i1, s=0..smax);

smax := 20;  R := 1680;  k := 1/4;  gam := 1/2;

The preceding response seemed to have several Maple statements that were not actually involved in the solution, making it difficult to follow the applied scheme of that solution.

      Thanks in advance,     John Ogilvie

Why is this integral so difficult -- so slow to execute?

seq(evalf(Int(1/R*sinh(s*coth(1/2*s))^(2*I/k)/(gam-I*k*cosh(s))^5*
     Int(exp(-(k^2*sinh(s)^2/(gam-I*k*cosh(s))-I*k*(1+cosh(s)))*v)*
     hypergeom([1/k*I],[1],k*v*I)*v^n,v = 0 .. 1/2*R), s=0..s_max)), n=0..1);

Hints to improve the efficiency of execution would be appreciated.

This simple set of integrations works correctly and quickly in Maple 17 and other releases, but not in Maple 2020.

psi(x) := (-1)^v*(alpha*GAMMA(k-v)/v!/GAMMA(k-2*v-1)/GAMMA(k-2*v))^(1/2)*exp(-1/2*k*exp(-alpha*x))*                 (k*exp(-alpha*x))^(1/2*k-v-1/2)*LaguerreL(v,k-2*v-1,k/exp(alpha*x))/binomial(k-v-1,v);

Int(eval(%, [k=30.5, v=j, alpha=2.5])^2, x=-1..infinity) =
   seq(evalf[12](Int(eval(%, [k=30.5, v=j, alpha=2.5])^2, x=-1..infinity)), j=0..5);

Every time that I try this simple integration in Maple 2020 I receive a message "kernel connection lost".  Why???

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