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

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

#### TKHunny

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.

Oh... and how can I make Maple assume that 'x' is a real symbol?

#### TKHunny

There should be an "Assume" paremeter. Something like (assume,x=real)

#### scorpion007

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

CaptainBlack