Does anyone know of a java library or algorithm for efficiently implementing the second Chebyshev function?

To be clear, I'm refering to this expression:

$$\vartheta(x) = \sum_{p \le x}\log p$$

$$\psi(x) = \sum_{m=1}^{\infty}\vartheta\left(\sqrt[m]{x}\right)$$

where $\vartheta(x)$ is the first Chebyshev function and $\psi(x)$ is the second Chebyshev function?

Thanks very much,


  • 1
    $\begingroup$ There is a Perl library that has this function, chebyshev_psi. $\endgroup$ – hardmath May 7 '13 at 3:57

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