Thank you all for the friendly and helpful explanations - and for your patience. The solution to my problem is finally f :: Double -> Double f i = (-1)**i/(2**(10*i)) * (-2^5/(4*i+1)-1/(4*i+3)+2^8/(10*i+1) -2^6/(10*i+3)-2^2/(10*i+5)-2^2/(10*i+7)+1/(10*i+9)) I had confused (^) and (**) due the fact that 1.0/2^16 or (-1.0)^2/2^16 are accepted. The important sentence in the Gentle Tutorial is " It is easy to forget at times that numerals are overloaded, and not implicitly coerced to the various numeric types," (Finding my errors was made somewhat difficult due to the following messages I got while testing my conjectures: *Main> let i=1 in 1/2^i 0.5 *Main> let i=1 in i/2^i Ambiguous type variable `a' in these top-level constraints: `Fractional a' arising from use of `/' at <interactive>:1 `Integral a' arising from use of `^' at <interactive>:1 :-) ) Thanks to all. Marc Charpentier