Approximate formulas for some functions of prime numbers

Some Inversion Formulas and Formulas for Stirling Numbers

In the paper we present some new inversion formulas and two new formulas for Stirling numbers.

Some Computational Formulas for D-Nِrlund Numbers

and Applied Analysis 3 It follows from 1.11 or 1.12 that t n, k t n − 2, k − 2 − 1 4 n − 2 t n − 2, k , 1.13 and that t n, 0 δn,0 n ∈ N0 : N ∪ {0} , t n, n 1 n ∈ N , t n, k 0 n k odd , t n, k 0 k > n or k < 0 , 1.14 where δm,n denotes the Kronecker symbol. By 1.13 , we have t 2n 1, 1 −1 n 2n ! 42n ( 2n n ) , t 2n 2, 2 −1 n n! 2 n ∈ N0 , 1.15 t 2n 2, 4 −1 n 1 n! 2 ( 1 1 22 1 32 · · · 1 n2 ) n ∈ ...

Some Asymptotic Formulas for Multiplicative Functions

Some summation formulas involving harmonic numbers and generalized harmonic numbers

Some Asymptotic Formulas on Generalized Divisor Functions

1 . Throughout this paper, we use the following notation : c•1 , c2 , . . ., X0 , X1 , . . . denote positive absolute constants. We denote the number of elements of the finite set S by BSI . We write ex =exp (x) . We denote the least prime factor of n by p(n) . We write pall n if pain but pa+1 f n . v(n) denotes the number of the distinct prime factors of n, while the number of all the prime fa...