In this paper, we consider the degenerate Stirling polynomials of the second kind which are derived from the generating function. In addition, we give some new identities for these polynomials.2010 Mathematics Subject Classification. 11B68; 11S80.

This is first meta-analysis to evaluate cancer risk associated with secondhand smoking across all cancers. A literature search was conducted for articles published before June 2014 on Pubmed, SCOPUS, Cochrane library, and CINAHL, and 40 articles on secondhand smoke and the prevalence of cancer among never smokers were selected for final analysis as per the inclusion criteria. Of the 40 articles, 27 were case-control studies and 13 were prospective cohort studies. With respect to overall cancer risk, odds ratio (OR) involving never smokers with significant exposure to secondhand smoke compared to never smokers without such exposure was 1.163 (95%CI 1.058–1.279). Subgroup meta-analyses by study design showed significant positive associations for both case-control studies and prospective cohort studies (OR 1.165, 95%CI 1.029–1.320; and OR 1.160, 95%CI 1.002–1.343, respectively). The association was stronger in the case of females (OR 1.253, 95%CI 1.142–1.374), lung cancer (OR 1.245, 95%CI 1.026–1.511), and breast cancer (OR 1.235, 95%CI 1.102–1.385). Secondhand smoking may increase the overall risk of cancer for never smokers, particularly lung and breast cancer, and especially in women. Strict implementation of smoking cessation programs should be encouraged, not only to reduce active smoking but also to limit exposure to secondhand smoke.

The polyexponential functions were introduced by Hardy and rediscovered by Kim, as inverses to the polylogarithm functions. Recently, the type 2 poly-Bernoulli numbers and polynomials were defined by means of the polyexponential functions. In this paper, we introduce the degenerate polyexponential functions and the degenerate type 2 poly-Bernoulli numbers and polynomials, as degenerate versions of such functions and numbers and polynomials. We derive several explicit expressions and some identities for those numbers and polynomials.

Recently, Dolgy-Jang introduced the poly-Genocchi polynomials and numbers arising from the modified polyexponential function. In this paper, we study the degenerate poly-Genocchi polynomials and numbers constructed from the modified degenerate polyexponential function. We derive explicit expressions for those polynomials and numbers. Also, we obtain identities involving those polynomials and numbers and some other special numbers and polynomials. In addition, we investigate the higher-order degenerate Genocchi polynomials and find identities involving those polynomials and the higher-order Changhee polynomials.

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