On Euler products with smaller than one exponents

[1] M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Applied Mathematics Series 55, tenth printing, Dover publications, (1972).Search in Google Scholar

[2] T. M. Apostol Introduction to Analytic Number Theory, Undergraduate Texts in Mathematics, Springer-Verlag, (1976).10.1007/978-1-4757-5579-4Search in Google Scholar

[3] E. Bach, J. Shallit, Algorithmic Number Theory, Volume 1: Efficient Algorithms, The MIT Press, (1996).Search in Google Scholar

[4] R. W., Barnard, K. C. Richards, A Note on the Hypergeometric Mean Value, Comput. Meth. Funct. Th., 1 (1) (2001), 81–88.10.1007/BF03320978Search in Google Scholar

[5] B. C. Berndt, Ramanujan’s Notebooks, Part I., Springer, (1985).10.1007/978-1-4612-1088-7Search in Google Scholar

[6] B. C. Berndt, R. J. Evans, Some elegant approximations and asymptotic formulas of Ramanujan, J. Comput. Appl. Math., 37 (1991), 35–41.10.1016/0377-0427(91)90104-RSearch in Google Scholar

[7] R. P. Brent, On the Zeros of the Riemann Zeta Function in the Critical Strip. Math. Comp., 33 (148) (1979), 1361–1372.10.1090/S0025-5718-1979-0537983-2Search in Google Scholar

[8] B. C. Carlson, Some inequalities for hypergeometric functions. Proc. Amer. Math. Soc., 17 (1966), 32–39.10.1090/S0002-9939-1966-0188497-6Search in Google Scholar

[9] L. Euler, Variae observationes circa series infinitas. Commentarii academiae scientiarum Petropolitanae, 9 (1737), 160–188.Search in Google Scholar

[10] H. Koch, Sur la distribution des nombres premiers. Acta Math., 24 (1901), 159–182.Search in Google Scholar

[11] T. Kotnik, The prime-counting function and its analytic approximations, π(x) and its approximations. Adv. Comput. Math., 29 (1) (2008), 55–70.10.1007/s10444-007-9039-2Search in Google Scholar

[12] F. Mertens, Ein Beitrag zur analytischen Zahlentheorie, J. reine angew. Math., 78 (1874), 46–62.Search in Google Scholar

[13] K. C. Richards, Sharp power mean bounds for the Gaussian hypergeo-metric function. J. Math. Anal. Appl., 308 (1) (2005), 303–313.10.1016/j.jmaa.2005.01.018Search in Google Scholar

[14] L. Schoenfeld, Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x).II. Math. Comp., 30 (134) (1976), 337–360.10.1090/S0025-5718-1976-0457374-XSearch in Google Scholar