@Axel Vogt yup it is like that.... d(beta*h)/(beta*h)

@Axel Vogt yup it is like that.... d(beta*h)/(beta*h)

Dear Preben Alsholm, Thanks for your kind efforts, actually I put expression into 2D format but to avoid any mistakes I remove it, now I calculated the same but I wonder it still did't give me result as expected (poor accuracy). Anyway I am trying to get improved hopefully I'll get it and thanks again for your prompt replies & useful advices

Dear Preben Alsholm, Thanks for your kind efforts, actually I put expression into 2D format but to avoid any mistakes I remove it, now I calculated the same but I wonder it still did't give me result as expected (poor accuracy). Anyway I am trying to get improved hopefully I'll get it and thanks again for your prompt replies & useful advices

Thanks again, since u replied I tried it alot by giving my inputs into your composed file but still stuck :(

Yes I am using Maple 14, as i told you last time I have change some input values and now I have an equation

A := int((1.334389725*sin(1.199050000*beta)/beta+(1.669308692*(cos(1.199050000*beta)-1.667987156*sin(1.199050000*beta)/beta+2.782181154*sin(.5995250000*beta)^2/beta^2))/beta^2)^2/((61.09*(240.38915*tanh(.787*beta)*beta(.787*beta)+1))/(61.09+3.935*tanh(.787*beta)*beta(.787*beta))+1.7314*coth(.787*beta)*beta(.787*beta)), beta = 0 .. infinity)

and now I want to use same procedures

subs(beta(beta) = beta, A)
B := normal(%)
f := IntegrationTools:-GetIntegrand(B)
asympt(f, beta, 9)
series(f, beta = 0, 9)
plot(f, beta = 0 .. 100);
evalf(Int(f, beta = 0 .. 1000))

But I unable to take evalf using 0...1000 range for my required input equation, its giving me error!!! (i,e Error, (in asympt) unable to compute series) even in both files that you send me

Can u plz check and make corrections into attached file, and replied me back

Your First Message File - 1-first.mw 

Second Message File - 2second.mw

Thanks

Thanks again, since u replied I tried it alot by giving my inputs into your composed file but still stuck :(

Yes I am using Maple 14, as i told you last time I have change some input values and now I have an equation

A := int((1.334389725*sin(1.199050000*beta)/beta+(1.669308692*(cos(1.199050000*beta)-1.667987156*sin(1.199050000*beta)/beta+2.782181154*sin(.5995250000*beta)^2/beta^2))/beta^2)^2/((61.09*(240.38915*tanh(.787*beta)*beta(.787*beta)+1))/(61.09+3.935*tanh(.787*beta)*beta(.787*beta))+1.7314*coth(.787*beta)*beta(.787*beta)), beta = 0 .. infinity)

and now I want to use same procedures

subs(beta(beta) = beta, A)
B := normal(%)
f := IntegrationTools:-GetIntegrand(B)
asympt(f, beta, 9)
series(f, beta = 0, 9)
plot(f, beta = 0 .. 100);
evalf(Int(f, beta = 0 .. 1000))

But I unable to take evalf using 0...1000 range for my required input equation, its giving me error!!! (i,e Error, (in asympt) unable to compute series) even in both files that you send me

Can u plz check and make corrections into attached file, and replied me back

Your First Message File - 1-first.mw 

Second Message File - 2second.mw

Thanks

Thanks Preben Alsholm!

I have tried same as you described and found it very helpful, in first part I calculated for certain range, like 0-200000, then as you mentioned 

 More work could be done on this, of course. You could try something like:

evalf[15](Int(f,beta=0..10000,method = _d01akc));
#and
evalf[15](Int(f,beta=0..200000,method = _d01akc,epsilon=1e-10));
#for large values of beta f is bounded from above by
g:=eval(f,{sin=1,cos=1,tanh=1,coth=1,-38400.=38400});
#so you can get an upper bound for the error by computing:
evalf[15](Int(g,beta=200000..infinity));

from this, I also calculatee for 200000 to infinity range, but can u plz tell

1. to get for the whole range i.e 0-infinity, how could I do this, should I add both ranges value?
2. another thing when I changed some input it give some error so how could I fix it?  To_check.mw

Thanks 

Thanks Preben Alsholm!

I have tried same as you described and found it very helpful, in first part I calculated for certain range, like 0-200000, then as you mentioned 

 More work could be done on this, of course. You could try something like:

evalf[15](Int(f,beta=0..10000,method = _d01akc));
#and
evalf[15](Int(f,beta=0..200000,method = _d01akc,epsilon=1e-10));
#for large values of beta f is bounded from above by
g:=eval(f,{sin=1,cos=1,tanh=1,coth=1,-38400.=38400});
#so you can get an upper bound for the error by computing:
evalf[15](Int(g,beta=200000..infinity));

from this, I also calculatee for 200000 to infinity range, but can u plz tell

1. to get for the whole range i.e 0-infinity, how could I do this, should I add both ranges value?
2. another thing when I changed some input it give some error so how could I fix it?  To_check.mw

Thanks