In the framework of D. Kendall's theory of Delphic semigroups, a semigroup of series in Legendre functions of the second kind is studied. The basic factorization theorems are prowed, the classes of infinitely divisible elements and of elements without indecomposable factors are completely described, the density of the class of indecomposable elements is established.
D. Kendall's Delphic semigroup, infinitely divisible, indecomposable, Legendre functions.
Il'INSKAJA, I. P. (1997) "Arithmetic of a Semigroup of Series in Legendre Functions of the Second Kind," Turkish Journal of Mathematics: Vol. 21: No. 3, Article 12. Available at: https://journals.tubitak.gov.tr/math/vol21/iss3/12