Quasipower and hypergeometric series -- construction and evaluation (Q1904149)

To speed up convergence of a certain class of power series in the neighbourhood of the point \(x = 1\), the series are transformed into quasipower series, that are more complicated, but converge faster. The terms contain powers of \(x\) and Gauss hypergeometric functions with argument \(x\). The class of functions is of the form \(F(x) = \sum a_k x^k\), \(a_k = \sum^\infty_{j = r} b_j/(k + 1)_j\), where \(r > 1\) is a natural number and \((u)_j\) is Pochhammer's symbol. The method is analysed in detail for Euler's dilogarithm.