SeriesCoefficient: needs work!

*To*: mathgroup at smc.vnet.net*Subject*: [mg83384] SeriesCoefficient: needs work!*From*: jackgold at umich.edu*Date*: Mon, 19 Nov 2007 06:11:24 -0500 (EST)

Hi Everyone, I have been experimenting with the new (ver 6) command, SeriesCoefficient in the form, SeriesCoefficient[fnt,{x,x0,n}]. Here fnt is a function of x and n is symbolic. This command is supposed to return the nth coefficient in the series expansion of fnt about x0. I have found the following results on a MacBook Pro running Tiger. 1) SeriesCoefficient[Cos[x] Exp[x], {x, 0, n}] returns itself, unevaluated. 2) SeriesCoefficient[Cos[x] Exp[x]/(1-x), {x, 0, n}] returns an expression involving incomplete Gamma functions with an imaginary argument. Odd that 1) does not compute but 2) does! Not that the result is terribly revealing, by the way. 3) SeriesCoefficient[Sin[x] Exp[x], {x, 0, n}] so preposterously complicated that most of us would have preferred no result! (Just joking. The result is far to complicated to publish here.) My opinion is that this use of SeriesCoefficient should not be offered to the public until some of these obvious glitches are cleaned up. Incidentally, since the nth terms of the individual functions Sin[x], Cos[x], Exp[x] and 1/(1-x) can be found using SeriesCoefficient and surely Mathematica knows how to find the nth coefficient of a product of power series, I suspect the problem lies in the finite summation which results from the use of the Cauchy product formula.