7 citations · 9 across the 10 of their papers we have counts for
11 papers
Pi and the primes
Simon Plouffe
By using Beta Dirichlet series and then Eisenstein series we ca represent primes with first a good approximation and an exact expression. This can be done with arbitrary prime (up…
A formula for the decimal digit or binary of and powers of
Simon Plouffe
By using an asymptotic formula known for the numbers of Euler and Bernoulli it is possible to obtain an explicit expression of the nth digit of in decimal or in binary, it also…
The calculation of p_n and pi_n
Simon Plouffe
A new approach is presented for the calculation of p_n and pi_n which uses the Lambert W function. An approximation is first found and using a calculation technique it makes it pos…
A set of formulas for primes
Simon Plouffe
A new set of formulas for primes is presented. These formulas are more efficient and grow much slower than the two known formulas of Mills and Wright. 3 new formulas are explained.
On the values of the functions zeta and gamma
Simon Plouffe
An analysis of the zeta and gamma function is presented, using elementary functions like [] and {}, a general formula for the angle of zeta(1/2 + i*n) is found and the same for the…
Identities inspired from the Ramanujan Notebooks, first series (1998)
Simon Plouffe
I present here a collection of formulas inspired from the Ramanujan Notebooks. These formulas were found using an experimental method based on three widely available symbolic compu…