The paper discusses several mathematical issues related to the numerical calculation of entanglement amount present in states describing bipartite quantum systems. The novel aspect of the presented material is the use of the Fredholm determinants theory methods for computing the amount of entanglement through the use of several, entropy-based entanglement measures. In particular, the continuous variable systems case [30, 31] is covered properly by the obtained here results, including presentation of a suitable renormalisation procedure of extracting the finite part of entanglement (often arises a situation in which the value of the corresponding entropy is infinite). Particular attention has been paid to the application of so-called unified entropy variants known as Rényi, resp. Tsallis entropies in the region of parameter \(\alpha \) values in the interval (0, 1), where, in the case of infinitely dimensional systems, the infinite value of the corresponding unified entropy is very typical, even for frequently encountered quantum states. A library of functions supporting entropies and the corresponding entanglement calculations are also presented as an extension of the constructed by us EntDetector package for the Python language platform.