Mariusz Iwaniuk

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These are replies submitted by Mariusz Iwaniuk



I think the MMA gave the correct answer.

f := 1+r^2*(1-sqrt(1+20*lambda*M/r^5))/(6*lambda);

func := eval(simplify(lambda*(2*(diff(f, r, r))+4*(diff(f, r))/r)-1), [M = 1, lambda = 1]);

plot(func, r = -5 .. 5, view = [-5 .. 5, -2 .. 2]); # ?




Maple 2018.1 give a symbolic answer ,but is incorrect. Probably a bug.

Bulid-in pdsolve function can't solve symbolically or numerically  fractional nonlinear partial differential equation.


if x<0 and y<0;

is(eval(log(x)+log(y), [x = -3, y = -2]), eval(ln(x*y), [x = -3, y = -2]));



sum((-1)^l*binomial(n-r, l)*binomial(n+r+l+1, n-r)/(k+r+l+j+2), l = 0 .. n-r) assuming k::posint,r::posint,j::posint,n::posint;

#binomial(n+r+1, n-r)*hypergeom([-n+r, n+r+2, k+r+j+2], [2*r+2, k+r+3+j], 1)/(k+r+j+2)

(2*r+1)*(sum((-1)^j*binomial(n-k, j)*binomial(n+k+j+1, n-k)*(%)/(k+j+1), j = 0 .. n-k)) assuming k::posint,r::posint,n::posint;

# Input ?

Maple 2018.1 return  unevaluated for me.

Mathematica 11.3 also can't solve.


With Mathematica it easy to do.

In Maple it's not so easy:

1 page.


Maple have No  built-in collocation methods, least squares method, Galerkin method to solve ode's.

dsolve it have method `series`,but in your case dosen't work.



I made a mistake,Yes you are right for Z=4 sum is converge.

I check for i=100 and q=150.

This really isn't a question in the absence of a concrete cut-and-pastable example,

 Maple 18  is NOT up to date?


From Maple's help:

_d01ajc is for finite interval of integration; allows for badly behaved integrands;

uses adaptive Gauss 10-point and Kronrod 21-point rules.


"maxintervals=300000". Probably is the maximum number of subdivisions for a given interval.BTW for [0,1].

That's all I know how much is written in the Maple help.


On my Maple 2018.1 works fine.

On MMA 11.3:



It's normal behavior if you want a converged sum you must  increase again q.

I do not understand , why you tried approximate the sum?, after all, you already know the answer: 0.1404283142

Increase Digits to 20 and q to 120.

Probably it's a bug.I'm submit possible bug to SCR.



Put your question in and there they will tell you what 
I am telling you that it is impossible(No practical use)
Formula 15 will not help you because it is Laplace's Transform of the integral, 
and you have something else in the question.


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