Series Csc[z]

*To*: mathgroup at smc.vnet.net*Subject*: [mg77217] Series Csc[z]*From*: wjlee <wen.jau.lee at gmail.com>*Date*: Tue, 5 Jun 2007 07:04:25 -0400 (EDT)

Hello, The Series[Csc[z], {z, 0, 3}] gives 1/z + z/6 + 7/360*z^3 + O[z]^4 However the first few terms of the Laurent series expansion approximate well for z<=pi/2. it will need many terms (perhaps >300) for good approximation for region pi/2 < z < pi. Mathematica has a "Pade" function but depending on where the "centered around" point is, the solution is still rather complicated. Is there other Mathematica functions (or way to do it) that could give us nice Laurent series form but using less than 20 terms? Thanks. wj