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Mariusz Iwaniuk

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These are replies submitted by Mariusz Iwaniuk

....

Mariusz Iwaniuk 1571
July 24 2018
0 0

@radaar 

 

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

I check for i=100 and q=150.

PROBLEM1.mw

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Mariusz Iwaniuk 1571
July 21 2018
0 0

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

 Maple 18  is NOT up to date?

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Mariusz Iwaniuk 1571
July 21 2018
0 0

@digerdiga 

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.

AND:

"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.

Works fine...

Mariusz Iwaniuk 1571
July 20 2018
0 0

@kuwait1 

On my Maple 2018.1 works fine.

On MMA 11.3:

 

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Mariusz Iwaniuk 1571
July 20 2018
0 0

@kuwait1 

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

No_problem.mw

Increase......

Mariusz Iwaniuk 1571
July 20 2018
0 0

Increase Digits to 20 and q to 120.

Bug....

Mariusz Iwaniuk 1571
July 19 2018
0 0

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

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Mariusz Iwaniuk 1571
July 12 2018
0 0

@spalinowy 

 

Put your question in https://math.stackexchange.com 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.

 

@vv  I copy code,paste,execute,dos...

Mariusz Iwaniuk 1571
July 07 2018
0 0

@vv 

I copy code,paste,execute,dosen't work?

If I convert to 1D  then works. 

I'm confused.

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Mariusz Iwaniuk 1571
July 04 2018
0 0

@shimaa sadk 

On Maple 2018.1 yours attached file works fine.Maple calculate  all worksheet about 30 seconds.

See result:


 

NULL

> 

with(LinearAlgebra); with(VectorCalculus); with(Student[LinearAlgebra]); with(SignalProcessing); with(Statistics); with(IntegrationTools)
> 

NULL
> 

r[1] := int(lambda[1]*alpha^2*exp(lambda[1]*Z)/((exp(lambda[1]*Z)-1+alpha)^2*(exp(lambda[2]*Z)-1+alpha)), Z = 0 .. infinity)

int(lambda[1]*alpha^2*exp(lambda[1]*Z)/((exp(lambda[1]*Z)-1+alpha)^2*(exp(lambda[2]*Z)-1+alpha)), Z = 0 .. infinity)

 (1)
> 

NULL

``

> 

NULL
> 

> 

R[1] := Expand(diff(r[1], lambda[1])); R[1, 1] := diff(r[1], lambda[1], lambda[1]); R[1, 2] := diff(r[1], lambda[1], lambda[2]); R[1, 3] := diff(r[1], lambda[1], alpha); R[2] := diff(r[1], lambda[2]); R[2, 1] := diff(r[1], lambda[2], lambda[1]); R[2, 2] := diff(r[1], lambda[2], lambda[2]); R[2, 3] := diff(r[1], lambda[2], alpha); R[3] := diff(r[1], alpha); R[3, 1] := diff(r[1], alpha, lambda[1]); R[3, 2] := diff(r[1], alpha, lambda[2]); R[3, 3] := diff(r[1], alpha, alpha)
> 

NULL
> 

lambda[1] := 3/10; lambda[2] := 2*(1/10); alpha := 4
> 

aa[1] := 0; aa[2] := 0; aa[3] := 0; bb[1] := 0; bb[2] := 0; bb[3] := 0
> 

r_r[1] := Re(simplify(r[1]))

(1/27)*(6*3^(1/6)+10*3^(5/6))*arctan((2/3)*3^(1/6)-(1/3)*3^(1/2))+(1/27)*(15*3^(1/3)-3*3^(2/3))*ln(1+3^(1/3))+(2/9)*Pi*3^(1/2)-(1/9)*3^(1/6)*Pi-(5/27)*3^(5/6)*Pi-(10/27)*3^(1/3)*ln(2)+(2/27)*3^(2/3)*ln(2)+(2/3)*ln(2)+1/3

 (2)
> 

R_R[1] := Re(evalf(R[1])); R_R[1, 1] := Re(evalf(R[1, 1])); R_R[1, 2] := Re(evalf(R[1, 2])); R_R[1, 3] := Re(evalf(R[1, 3])); R_R[2] := Re(evalf(R[2])); R_R[2, 1] := Re(evalf(R[2, 1])); R_R[2, 2] := Re(evalf(R[2, 2])); R_R[2, 3] := Re(evalf(R[2, 3])); R_R[3] := Re(evalf(R[3])); R_R[3, 1] := Re(evalf(R[3, 1])); R_R[3, 2] := Re(evalf(R[3, 2])); R_R[3, 3] := Re(evalf(R[3, 3]))

Re(Expand(-10*dilog(1+((1/3)*I)*3^(1/2))+(100/9)*ln(2)-(10/81)*3^(1/3)*dilog(1+((1/2)*I)*3^(1/6)-(1/6)*3^(2/3))+(20/3)*dilog(1-((1/2)*I)*3^(1/6)-(1/6)*3^(2/3))-(40/729)*ln(3)*Pi*3^(5/6)-(520/243)*ln(3)*Pi*3^(1/6)-(10/81)*3^(1/3)*dilog(1-((1/2)*I)*3^(1/6)-(1/6)*3^(2/3))-(100/81)*arctan((2/3)*3^(1/6)-(1/3)*3^(1/2))*3^(5/6)+(130/81)*3^(2/3)*dilog(1+((1/2)*I)*3^(1/6)-(1/6)*3^(2/3))+(130/81)*3^(2/3)*dilog(1-((1/2)*I)*3^(1/6)-(1/6)*3^(2/3))+(5/3)*3^(1/2)*ln(3)*Pi-((130/27)*I)*3^(1/6)*dilog(1+((1/2)*I)*3^(1/6)-(1/6)*3^(2/3))+((130/27)*I)*3^(1/6)*dilog(1-((1/2)*I)*3^(1/6)-(1/6)*3^(2/3))+((10/3)*I)*dilog(1+((1/3)*I)*3^(1/2))*3^(1/2)-((10/3)*I)*dilog(1-((1/3)*I)*3^(1/2))*3^(1/2)+((10/81)*I)*3^(5/6)*dilog(1-((1/2)*I)*3^(1/6)-(1/6)*3^(2/3))-((10/81)*I)*3^(5/6)*dilog(1+((1/2)*I)*3^(1/6)-(1/6)*3^(2/3))-10*dilog(1-((1/3)*I)*3^(1/2))-(25/18)*ln(3)^2+(20/3)*dilog(1+((1/2)*I)*3^(1/6)-(1/6)*3^(2/3))-(260/81)*dilog(1+(1/3)*3^(2/3))*3^(2/3)+(20/81)*dilog(1+(1/3)*3^(2/3))*3^(1/3)-(10/81)*ln(1-3^(1/3)+3^(2/3))*3^(2/3)-(100/81)*ln(1+3^(1/3))*3^(1/3)+(50/81)*ln(1-3^(1/3)+3^(2/3))*3^(1/3)+(20/27)*Pi*3^(1/2)-(25/54)*Pi^2+(20/3)*dilog(1+(1/3)*3^(2/3))+(20/81)*ln(1+3^(1/3))*3^(2/3)-(20/27)*arctan((2/3)*3^(1/6)-(1/3)*3^(1/2))*3^(1/6)-(520/729)*3^(2/3)*Pi^2+(40/729)*3^(1/3)*Pi^2+(50/81)*3^(5/6)*Pi+(10/27)*3^(1/6)*Pi))

  

-5.223468552

  

2.445216045

  

0.58653935e-1

  

-1.616996031

  

2.445216045

  

4.417156107

  

-0.87980902e-1

  

0.88621008e-2

  

0.58653935e-1

  

-0.87980902e-1

  

-0.16512086e-2

 (3)
> 

NULL


 

Download aquestion_(2).mw

 

If you have problem then  try this worksheet below:

aquestion_(1)_ver2.mw

....

Mariusz Iwaniuk 1571
July 04 2018
0 0

@shimaa sadk 

For general integral with general constans :

int(lambda[1]*alpha^2*exp(lambda[1]*Z)/((exp(lambda[1]*Z)-1+alpha)^2*(exp(lambda[2]*Z)-1+alpha)), Z = 0 .. infinity)

Maple 2018.1 can't find symbolic solution.

r[1] := proc (lambda1, lambda2, alpha) options operator, arrow; lambda1*alpha^2*exp(lambda1*Z)/((exp(lambda1*Z)-1+alpha)^2*(exp(lambda2*Z)-1+alpha)) end proc;
R[1] := int(eval(diff(r[1](lambda1, lambda2, alpha), lambda1), [lambda1 = 3/10, lambda2 = 2*(1/10), alpha = 4]), Z = 0 .. infinity, numeric);


#R[1] := 1.077997357

 

See attached file for more information:

aquestion_(1).mw

Only comment....

Mariusz Iwaniuk 1571
June 30 2018
0 0

@spalinowy 

I gave you only a comment,my point of view. Wait for the answer.

And so at the end you'll end up with numerical calculations.

....

Mariusz Iwaniuk 1571
June 30 2018
0 0

You have a Transcendental equations that why Maple can't solve(Any CAS can't solve).Transcendental equations have no analytical solution.

Try numeric solver like fsolve, DirectSearch package,or something else.

 

See:https://en.wikipedia.org/wiki/Transcendental_equation

        https://www.mapleprimes.com/questions/88377-Direct-Search-Optimization-Package

....

Mariusz Iwaniuk 1571
June 20 2018
0 0

@digerdiga 

I updated my answer.Its the same answer like done by  the user Carl Love.Probably a better simplification can not be done.

Ei_ver2.mw

Workaround....

Mariusz Iwaniuk 1571
June 12 2018
0 0

@digerdiga 

restart;

assume(R::real, z::real); is(-R+sqrt(R^2+z^2) < 0);

#false

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