We examine series of the form In each case, there is an evaluation of the form (pm(x)f(x)-qm(x))/x2m where f(x) is a transcendental function and pm(x) and qm(x) are polynomials with rational coefficients. We prove that for |x|<1, From this result, we derive recurrences for π and for various logarithms.
|Original language||English (US)|
|Number of pages||13|
|Journal||Missouri Journal of Mathematical Sciences|
|State||Published - Jun 6 2013|