We analyze the problem of global reconstruction functions as accurately possible, based on partial information in form a truncated power series at some point, and additional analyticity properties. This situation occurs frequently applications. The question optimal procedure was open, we formulate it well-posed mathematical problem. Its solution leads to practical method which provides dramatic...

Let $$T(q) = \sum\limits_{k 1}^\infty {d(k){q^k},\,\,\,\,\left| q \right| < 1,} $$ where d(k) denotes the number of positive divisors natural k. We present monotonicity properties functions defined in terms T. More specifically, we prove that $$H(q) T(q) - {{\log (1 q)} \over {\log (q)}}$$ is strictly increasing on (0, 1), while $$F(q) {{1 q} q}H(q)$$ decreasing 1). These results are then ap...

In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad ‎et al., ‎‎[K. Maleknejad ‎and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, ‎Appl. Math. Comput.‎ (2005)]‎ to gain...