Maple : Is it really that hard to realize that sin(pi)=0 ?!

Jul 2009
168
3
I have an annoying problem in Maple.

I wanted maple to calculate the \(\displaystyle 10^th\) taylor series of f(x), while:

\(\displaystyle f(x):=\frac{1}{2\pi}\int^{\pi}_0 e^{xcos(t)} dt\)

and so I wrote :

f := (int(exp(x*cos(t)), t = 0 .. pi))/(2*pi)
p10 := taylor(f, x = 0, 11)

And I got an answer that involved multiplying by \(\displaystyle sin(\pi)\). I must change all these into zeros, so I tried to use the 'subs' command, or to simplify, even 'simplify trig', but it didn't change a thing.

What can I do in order to get a simple answer?

Thank you :)
 
Aug 2007
3,171
860
USA
The sine function is single-valued only in the Real world.

Try forcing Maple to assume that 'x' is Real. You should be able to do this with a Symbolic Modifier.
 
Jul 2009
168
3
Oh... and how can I make Maple assume that 'x' is a real symbol?
 
Aug 2007
3,171
860
USA
There should be an "Assume" paremeter. Something like (assume,x=real)
 
Jul 2006
364
44
You have to use Pi not pi, because pi is just a symbol, whereas Pi is the constant 3.14...

Code:
sin(Pi);
                                      0
sin(pi);
                                   sin(pi)
Code:
f := (int(exp(x*cos(t)), t = 0 .. Pi))/(2*Pi);
                         int(exp(x cos(t)), t = 0 .. Pi)
                    f := -------------------------------
                                      2 Pi              
p10 := taylor(f, x = 0, 11);
          1   1  2    1   4    1    6     1     8      1      10    / 11\
   p10 := - + - x  + --- x  + ---- x  + ------ x  + -------- x   + O\x  /
          2   8      128      4608      294912      29491200
 
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