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Since the constructions of p-adic q-integrals, these integrals as well as particular cases have been used not only as integral representations of many special functions, polynomials, and numbers, but they also allow for deep examinations of many families of special numbers and polynomials, such as central Fubini, Bernoulli, central Bell, and Changhee numbers and polynomials. One of the key applications of these integrals is for obtaining the symmetric identities of certain special polynomials. In this study, we focus on a novel generalization of degenerate central Fubini polynomials. First, we introduce two variable degenerate w-torsion central Fubini polynomials by means of their exponential generating function. Then, we provide a fermionic p-adic integral representation of these polynomials. Through this representation, we investigate several symmetric identities for these polynomials using special p-adic integral techniques. Also, using series manipulation methods, we obtain an identity of symmetry for the two variable degenerate w-torsion central Fubini polynomials. Finally, we provide a representation of the degenerate differential operator on the two variable degenerate w-torsion central Fubini polynomials related to the degenerate central factorial polynomials of the second kind. [ABSTRACT FROM AUTHOR]

Background: The literature on the use of inflammatory indexes for palliative care patients without malignancy is scarce. Aims: To determine which inflammatory indexes are associated with the mortality risks of non-malignant patients hospitalised and receiving palliative care. Methods: Discharged or deceased patients in a palliative care unit of a secondary care hospital were included. The laboratory values were obtained during the first 48 hours of hospitalisation. Findings: As a result of univariate Cox regression analysis, 14-day mortality rate was affected by lymphocyte ratio, neutrophil-to-albumin ratio (NAR), C-reactive protein/albumin ratio (CAR), multi-inflammatory indexes (MII-1) and MII-2 (p<0.001, p=0.001, p=0.002, p=0.009 and p=0.003, respectively); NLR, CLR, NAR, CAR, MII-1 and MII-2 (respectively p=0.005, p<0.001, p<0.001, p<0.001, p=0.001 and p<0.001) affected 28-day mortality rate. Indexes that statistically significantly increased both 14-day and 28-day mortality rates independently of other variables were CLR, NAR, CAR, MII-1 and MII-2. Conclusion: High values in inflammatory indexes, including C-reactive protein and albumin increase the risk of 14-day and 28-day mortality rates in palliative care non-malignant patients. [ABSTRACT FROM AUTHOR]

After constructions of p-adic q-integrals, in recent years, these integrals with some of their special cases have not only been utilized as integral representations of many special numbers, polynomials, and functions but have also given the chance for deep analysis of many families of special polynomials and numbers, such as Bernoulli, Fubini, Bell, and Changhee polynomials and numbers. One of the main applications of these integrals is to obtain symmetric identities for the special polynomials. In this study, we focus on a novel extension of the degenerate Fubini polynomials and on obtaining some symmetric identities for them. First, we introduce the two-variable degenerate w-torsion Fubini polynomials by means of their exponential generating function. Then, we provide a fermionic p-adic integral representation of these polynomials. By this representation, we derive some new symmetric identities for these polynomials, using some special p-adic integral techniques. Lastly, by using some series manipulation techniques, we obtain more identities of symmetry for the two variable degenerate w-torsion Fubini polynomials. [ABSTRACT FROM AUTHOR]

Two new extensions of the familiar Bernoulli polynomials are considered by using q-sine, q-cosine, q-hypergeometric and q-exponential functions. We call q-sine and q-cosine hypergeometric Bernoulli polynomials. Then, diverse formulas and properties for these polynomials, such as summation formulas, addition formulas, q-derivative properties, q-integral representations and some correlations are derived. Also, q-sine and q-cosine hypergeometric Bernoulli polynomials with two parameters are introduced and some relations and identities are investigated. Furthermore, some computational values are given by tables, and the beautiful zeros representations of the q-sine hypergeometric Bernoulli polynomials and q-cosine hypergeometric Bernoulli polynomials are showed by the figures. [ABSTRACT FROM AUTHOR]

In this study, we introduce sine and cosine Bell-based Frobenius-type Eulerian polynomials, and by presenting several relations and applications, we analyze certain properties. Our first step is to obtain diverse relations and formulas that cover summation formulas, addition formulas, relations with earlier polynomials in the literature, and differentiation rules. Finally, after determining the first few zero values of the Eulerian polynomials, we draw graphical representations of these zero values. [ABSTRACT FROM AUTHOR]

In this paper, the authors consider the Carlitz's generalized twisted q-Bernoulli polynomials attached to χ and investigate some novel symmetric identities for these polynomials arising from the p-adic q-integral on Zp under S3.

In this work, we consider the degenerate Frobenius-Euler-Genocchi polynomials utilizing the degenerate exponential function and the degenerate Changhee-Frobenius-Euler-Genocchi polynomials utilizing the degenerate logarithm function. Then, we analyze some summation and addition formulas for these polynomials. In addition, we derive some correlations with degenerate Stirling numbers of both kinds and degenerate Frobenius-Euler polynomials. Moreover, we present difference and derivative operator rules for the generalized degenerate Frobenius-Euler-Genocchi polynomials. Lastly, we show certain zeros of both the degenerate Frobenius-Euler-Genocchi polynomials and the degenerate Changhee-Frobenius-Euler-Genocchi polynomials and provide their beautifully graphical representations. [ABSTRACT FROM AUTHOR]

In this paper, the Gould-Hopper based fully degenerate type2 poly-Stirling polynomials of the first kind with a q parameter are considered and some of their diverse identities and properties are investigated. Then, the Gould-Hopper based fully degenerate type2 poly-Bernoulli polynomials with a q parameter are introduced and some of their properties are analyzed and derived. Furthermore, several formulas and relations covering implicit summation formulas, recurrence relations and symmetric property are attained. [ABSTRACT FROM AUTHOR]

In this paper, the higher-order type 2 Daehee polynomials are introduced and some of their relations and properties are derived. Then, some p-adic integral representations of not only higher-order type 2 Daehee polynomials and numbers but also type 2 Daehee polynomials and numbers are acquired. Several identities and relations related to both central factorial numbers of the second kind and Stirling numbers of the first and second kinds are investigated. Moreover, the conjugate higher-order type 2 Daehee polynomials are considered and some correlations covering the type 2 Daehee polynomials of order β and the conjugate higher-order type 2 Daehee polynomials are attained. [ABSTRACT FROM AUTHOR]

Utilizing p , q -numbers and p , q -concepts, in 2016, Duran et al. considered p , q -Genocchi numbers and polynomials, p , q -Bernoulli numbers and polynomials and p , q -Euler polynomials and numbers and provided multifarious formulas and properties for these polynomials. Inspired and motivated by this consideration, many authors have introduced (p , q) -special polynomials and numbers and have described some of their properties and applications. In this paper, using the (p , q) -cosine polynomials and (p , q) -sine polynomials, we consider a novel kinds of (p , q) -extensions of geometric polynomials and acquire several properties and identities by making use of some series manipulation methods. Furthermore, we compute the p , q -integral representations and p , q -derivative operator rules for the new polynomials. Additionally, we determine the movements of the approximate zerosof the two mentioned polynomials in a complex plane, utilizing the Newton method, and we illustrate them using figures. [ABSTRACT FROM AUTHOR]