@Carl Love  

Thanks a lot for your so detailed explanation.

I found dsolve( ) is almost impossible to be stopped by the red stop button and I have to use task manager to kill the process every time .Very unfortunately, dsolve( ) is one of the most frequently used commands for me.I really hate to use this violent way to stop Maple.

@Preben Alsholm 

I' ve assumed that at the very beginning. 

@Carl Love 

Thanks! It works!

By the way, how can I stop Maple when a calculation takes too much time and I don’t
want it to be continued. I found it’s useless to press the red stop button on
the toolbar.   

@acer 

Is there any way to make dsolve ( ) directly return this answer?

@Alejandro Jakubi 

Thanks !

Is there anyway to limit the problem on the RealRange(Open(0), infinity), so the solution can be directly returned?

@maple fan 

If we limit the problem in the real domain, the domain of definition of the integrand is different from the solution.

@Axel Vogt 

Thanks!

Is there anyway to limit the problem on the RealRange(Open(0), infinity)?

@roman_pearce 

Thanks a lot for your so detailed reply!

But I still have a question, according to the help document, PiFast43 also use hypergeometric series to calculate Pi, why the performance is so different?

Is there any workaround ？

@Markiyan Hirnyk 

Maple can do lots of things, of course, but if it does faster, it’s better.

I suspects Maple 2015 doesn’t utilize the new libraries of functions such as Intel Integrated Performance Primitives and the new CPU Instruction Set Extensions such as AVX 2.0 to accelerate the calculation.

The example in this post is just to illustrate the problem in the most obvious way.

For lots of calculations, the elapsed time for Westmere Core i3 and Haswell Core i7 is almost the same.

@Markiyan Hirnyk 

Thanks a lot!

But is there any way somehow to calculate the closed-form solution of it?

@Markiyan Hirnyk 

@Markiyan Hirnyk 

See you again!

Thanks a lot for your reply, but it seems Maple 18 can’t solve the following equation within the ability of my laptop with i5 CPU and 8Gb RAM.

It just consumes the system resources, especially memory, crazily and can’t solve it within an hour. I deem it’s rather strange. 

 ///

restart;

eq := 2*b+5*cos(a)+I*(a+3*sin(b)) = 5+2*I;

solve(evalc(`~`[{Im, Re}](eq)))

///

@Preben Alsholm 

Sorry, my reply on the warning is actually for another guy in this post.

I think there must be something wrong with this reply, so it goes to you.

Your answer is really wonderful!

@Preben Alsholm 

Just as toandhsp described.