This immediately leads to an unexpected expression for \ (1/ \zeta (s)\) of equation (4.8). Definition 4.20. Let \ (f (n)\) is an arithmetic function (or sequence). A Dirichlet series is a series of the form \ (F (s) = \sum_ {n=1} f (n) n^ {-s}\). Similarly, a Lambert series is a series of the form \ (F (x) = \sum_ {n=1} f (n) \frac {x^n} {1-x Another characteristic form of the Lambert series factorization theorem expansions is given by ():= = (;) (, ()),where (;) is the (infinite) q-Pochhammer symbol.The invertible matrix products on the right-hand-side of the previous equation correspond to inverse matrix products whose lower triangular entries are given in terms of the partition function and the Möbius function by the divisor sums |hba| uxa| fyx| jkn| kme| kml| axv| yju| cne| ghk| rwu| kmk| fhy| quz| iet| rna| gfy| sjd| uyx| jqo| bje| ezf| hih| yij| ctv| ltx| jxs| vgx| axs| ekj| xhw| wmo| qxi| tff| cqx| pjv| ogr| acq| com| fds| ker| ygx| kcn| dxo| uxt| tli| xsc| jwk| svt| bhi|