Об иррациональностях, порожденных арифметическими прогрессиями

New irrational numbers decompositions into ordinary continued fractions (OCF) in the form of $\textit{b, a + b, ..., an + b, ... }$and into called completely almost periodic OCF of the first rank in the form [$a_0$, ..., $a_m$, $d$, $b_0$, ..., $b_k$, $c + d$, $b_0$, ...$b_k$, ... ] were obtained with the help of suggested parametric generalization of Eiler’s method. The description of all irrationalities decomposed into OCF of indicated types was given. Besides it was obtained the decompositions of some transcendental functions into more general P-fractions.