Re: Another integer-like transcendental number

TCL wrote:

> Let a=1/10, b=sqrt(2)/20. Then
> 
> cos(a)+cosh(a)+2cos(b)cosh(b)=4.000000000000992.....
> 
> Can anyone explain this one? Or give a reference.

cos(a) + cosh(a) = 2 (1 + a^4/4! + a^8/8! + ...)
cos(b)cosh(b) = 1 - b^4/6 + b^8/2520 + ... .

If a^4 = 4 b^4 (as it is here) then
cos(a) + cosh(a) + 2 cos(b)cosh(b) = 4 + b^8/1008 + ...
is very close to 4 if b (and so a) is small.

-- 
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
"Needless to say, I had the last laugh."
 Alan Partridge, _Bouncing Back_ (14 times)