r1:=2*(1-s^2)^(1/2)*arctanh((1+s)*tanh(x)/((1-s)*(1+s))^(1/2))/((1-s)*(1+s))^(1/2)+ln((1/2)*arccosh(1/s)-x)

with x=1/2*arccosh(1/s)-beta*u

is to be calculated to the first order in u.

in fact im only interested in the first order not in the zero order.

so when applying the series I get for the first order

-beta*u/sqrt(1-s^2)

whereas by hand I get:

-beta*u*s/sqrt(1-s^2)

 I'd really appreciate some idea since...

this function:

2*arctanh((1+s)*tanh(x)/sqrt((1-s)*(1+s)))+ln((1/2)*arccosh(1/s)-x)

shall be calculated @ x=1/2*arccosh(1/s)

when taking the limit maple tells me its 0

whereas when calculating it by hand i get ln(sqrt(1-s^2)/s)

whats the problem?

PS: 0<s<1

my function is:

f := proc (x) if 0 < x and x < evalf(Pi) then 1 elif evalf(Pi) < x and x < evalf(2*Pi) then -1 end if end proc

now it tried:

f1 := add((-1)^n*f(x-evalf(2*n*Pi)), n = 0 .. 10)

to get a periodic function.

but unfortunately it says:

Error, (in f) cannot determine if this expression is true or false: 0 < x and x < 3.141592654

already when trying to calc the sum.

Hey,

I have some expression of the form

sqrt((a+b)*(a-b))/(sqrt(a^2-b^2))

which maple unfortuntely does not simplify...

I have tried assumptions as a>0 b

how can one make this work?