## 263 Reputation

19 years, 36 days

## Why does this integral evaluate as "unde...

Maple 2021

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.

## How do I solve this sum over an infinite...

Maple 2021

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

(mathematica solves this instantly.)

## difficult integral revised...

Maple 2021

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.

## difficult numerical integration...

Maple 2021

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.

## Why loss of kernel connection?...

Maple 2020

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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