Geodesic
A lower bound for a~quotient of roots of factorials
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2009), pp. 64-69.

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With the aid of asymptotic properties of polygamma functions a new lower bound is established for the quotient $\phi(r+1)/\phi(r)$ where $\phi(r)=(r!)^{1/r}$. 
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Cristinel Mortici. A lower bound for a~quotient of roots of factorials. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2009), pp. 64-69. http://geodesic.mathdoc.fr/item/BASM_2009_3_a6/

[1] Abramowitz M., Stegun I. A., Handbook of Mathematical Functions, Dover publications, New York, 1965

[2] Artin E., The Gamma Function, Translated by Michael Butler. Athena Series: Selected Topics in Mathematics, Holt, Rinehart and Winston, New York, 1964 | MR | Zbl

[3] Bohr Y., Mollerup J., Laerebog i matematisk Analyse, v. III, Funktioner af flere reelle Variable, Jul. Gjellerups Forlag, Copenhagen, 1922

[4] Brégman L. M., “Some properties of nonnegative matrices and their permanents”, Soviet Math. Dokl., 14 (1973), 945–949 | Zbl

[5] Brualdi R. A., Ryser Y. J., Combinatorial Matrix Theory, Cambridge University Press, 1991 | MR | Zbl

[6] Choczewski D., Wach-Michalik A., “A difference equation for $q$-gamma functions”, Colloquium on Differential and Difference Equations, CDDE 2002 (Brno, 2002), Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math., 13, Masaryk Univ., Brno, 2003, 71–75 | MR | Zbl

[7] Dubourdieu J., “Sur un théorème de M. S. Bernstein relatif á la transformation de Laplace-Stieltjes”, Compositio Math., 7 (1939), 96–111 | MR | Zbl

[8] Hausdorff F., “Summationsmethoden und Momentfolgen, I”, Math. Z., 9 (1921), 74–109 | DOI | MR | Zbl

[9] Liang H., Bai F., “An upper bound for the permanent of $(0,1)$-matrices”, Linear Algebra Appl., 377 (2004), 291–295 | DOI | MR | Zbl

[10] Minc H., “Upper bound for permanents of $(0,1)$-matrices”, Bull. Amer. Math. Soc., 69 (1963), 789–791 | DOI | MR | Zbl

[11] Minc H., Permanents, Encyclopedia Math. Appl., 6, 1978 | MR | Zbl

[12] Minc H., Sathre L., “Some inequalities involving $(r!)^{1/r}$”, Proc. Edinburgh Math. Soc., 14:2 (1964–1965), 41–46 | DOI | MR | Zbl

[13] Mortici C., “An ultimate extremely accurate of the factorial function”, Arch. Math. (Basel), 93:1 (2009), 137–144 | DOI | MR

[14] Rasmussen L. E., “Approximating the permanent: a simple approach”, Random Structures Algorithms, 5 (1994), 349–361 | DOI | MR | Zbl

[15] Schrijver A., “Bounds on permanents, and the number of 1-factors and 1-factorizations of bipartite graphs”, Surveys in combinatorics (Southampton, 1983), London Math. Soc. Lecture Note Ser., 82, Cambridge Univ. Press, Cambridge, 1983, 107–134 | MR

[16] Valliant L., “The complexity of computing the permanent”, Theoret. Comput. Sci., 8 (1979), 189–201 | DOI | MR

[17] Zagaglia-Salvi N., “Permanents and determinants of circulant $(0;1)$-matrices”, Matematiche (Catania), 39 (1984), 213–219 | MR | Zbl

[18] Widder D. V., The Laplace Transform, Princeton Univ. Press, Princeton, NJ, 1941 | MR | Zbl