==Engel expansions for some well-known constants==:formula_17 = {1, 1, 1, 8, 8, 17, 19, 300, 1991, 2492...}:formula_18 = {1, 3, 5, 5, 16, 18, 78, 102, 120, 144...}:formula_19 = {1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13...}And in general,:formula_20More Engel expansions for constants can be found here.
На этот вопрос ответили Эрдёш и доказав, что число членов разложения равно O("y"1/3 + ε) для любого ε > 0.:formula_17 = {1, 1, 1, 8, 8, 17, 19, 300, 1991, 2492...} ():formula_18 = {1, 3, 5, 5, 16, 18, 78, 102, 120, 144...} ():formula_19 = {1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13...} ():formula_20Коэффициенты "ai" разложения Энгеля, как правило, имеют экспоненциальный рост.