- #1
camilus
- 146
- 0
I'm a bit confused as to how to calculate the 2nd chebyshev function.
I know [tex]\psi (x) = \sum_{p^k \le x} \ln p[/tex]
but can someone show me how to expand it? Like, do I use for 2^k, 2, 4, 8, 16, 32... for all the [tex]p^k \le x[/tex], same with 3, and 4 and so on?
MW gives the example:
[tex]\psi (10) = \ln (2520) = 3\ln2+2\ln3+\ln5+\ln7[/tex]
how would say, [tex]\psi (30)[/tex] be written?
I know [tex]\psi (x) = \sum_{p^k \le x} \ln p[/tex]
but can someone show me how to expand it? Like, do I use for 2^k, 2, 4, 8, 16, 32... for all the [tex]p^k \le x[/tex], same with 3, and 4 and so on?
MW gives the example:
[tex]\psi (10) = \ln (2520) = 3\ln2+2\ln3+\ln5+\ln7[/tex]
how would say, [tex]\psi (30)[/tex] be written?