Need a really advanced Calculus book

[AdrianZ]

I'm looking for an advanced Calculus book that explains special (non-elementary) functions and their properties and applications (like Lambert W function, elliptic functions, error function, Ei and other special functions). I'd also like it to contain different methods of integration like contour integration and differentiation under the integral sign.

 

[marcusl]

Much of what you are looking for is covered in Whittaker and Watson's Modern Analysis.

 

[mathwonk]

i don't know if it has all this but i suggest you look at apostol's mathematical analysis.