The author updates the state of knowledge about the origins of Polish coinage in the late tenth and early eleventh centuries. This became possible due to new coin finds and the use of new research methods and, above all, revealing new die-links. The author concludes that it was not Mieszko I (c. 962–992), but his son Boleslaus the Brave (992–1025) who began Polish coinage. This early coinage was more intensely produced and more diverse than was previously thought. In one mint, correctly inscribed dies and corrupted imitations of foreign patterns were used simultaneously. Coins served the purpose of both propaganda and economic tools. They accounted for a small proportion of the prevailing foreign coins in circulation.

In this article we analyse various methods of value approximation for Prolate Spheroidal Wave Functions (PSWF). As PSWFs are not given by explicit formula, for any application their values need to be calculated based on their properties and connection to other functions. We will focus on three approaches – Legendre polynomials, Eigenvalues of Matrix Operators and Hermite functions. We then create an implementation and test its effectiveness by using is as a base for band limited signal approximation algorithm.