Primes and the Lambert W function

M. Cipolla, “La determinazione assintotica dell’ n i ​ m ​ o n^{imo} numero primo”, Matematiche Napoli, 3

1902

Earlier work this paper cites.

J. Barkley Rosser, “The n n ’th Prime is Greater than n ​ ln ⁡ n n\ln n ”, Proc. London Math. Soc. 45

1938

Earlier work this paper cites.

J. Barkley Rosser, “Explicit Bounds for some functions of prime numbers”, American Journal of Mathematics, 63

1941

Earlier work this paper cites.

J. Barkley Rosser and Lowell Schoenfeld, “Approximate Formulas for Some Functions of Prime Numbers”, Illinois J. Math. 6

Original

1962

Earlier work this paper cites.

Ribenboim, P. The Little Book of Big Primes , (Springer-Verlag, New York, 1991)

1991

Earlier work this paper cites.

Corless, R. M.; Gonnet, G. H.; Hare, D. E. G.; Jeffrey, D. J.; and Knuth, D. E., “On the Lambert W W function”, Advances in Computational Mathematics 5

1996

Cited alongside, same era.

Ribenboim, P. The New Book of Prime Number Records , (Springer-Verlag, New York, 1996)

1996

Cited alongside, same era.

S. R. Valluri, D. J. Jeffrey, R. M. Corless, “Some Applications of the Lambert W W Function to Physics”, Canadian Journal of Physics 78

2000

Cited alongside, same era.

Petarpa Boonserm and Matt Visser, “Bounding the greybody factors for Schwarzschild black holes”, Phys. Rev. D 78

Original

2008

Cited alongside, same era.

Pierre Dusart, “The k t ​ h k^{th} prime is greater than k ⁡ ( ln ⁡ k + ln ⁡ ln ⁡ k − 1 ) k(\ln k+\ln\ln k-1) for k ≥ 2 k\geq 2 ”, Mathematics of Computation 68

Cited in the paper.

S. R. Valluri, M. Gil, D. J. Jeffrey, and Shantanu Basu, “The Lambert W W function and quantum statistics”, Journal of Mathematical Physics 50

2009

Later among the works it cites.

Seán M Stewart, “Wien peaks and the Lambert W W function”, Revista Brasileira de Ensino de Física 33

2011

Later among the works it cites.

Alexandre Vial, “Fall with linear drag and Wien’s displacement law: approximate solution and Lambert function”, European Journal of Physics, 33

2012

Later among the works it cites.

Seán M. Stewart, “Spectral Peaks and Wien’s Displacement Law”, Journal of Thermophysics and Heat Transfer, 26

2012

Later among the works it cites.