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In this paper, we evaluate two parameters hk,n and h ' k,n of some P-Q type Theta functions ϕ(q) for any positive real numbers k and n. During this process, we also evaluate Ramanujan's cubic continued fraction. [ABSTRACT FROM AUTHOR]

In this paper we give a representation formula for the general solution to the following two-dimensional system of difference equations ... where parameters a,b and initial values x-2,x-1,x0,y-2,y-1,y0 are real numbers. We also give some theoretical explanations related to the representation. [ABSTRACT FROM AUTHOR]

In this paper, by using umbral calculus and umbral algebra methods, we derive several interesting identities and relations related to the modified and unification of the Bernoulli, Euler and Genocchi polynomials and numbers and the generalized (β-) Stirling numbers of the second kind. We also give some applications and remarks related to these numbers and polynomials. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to investigate the behavior of the solution of the following max type difference equation of order three xn+1 = max{An/xn,xn-2} , n = 0, 1,. . ., where the initial conditions x-2, x-1, x0 are arbitrary positive real numbers and {An}n=0∝ is a periodic sequence of period two. [ABSTRACT FROM AUTHOR]

In this paper we have introduced the concept of geometric convergence of a sequence and determined the necessary and sufficient condition under which convergence follows from geometric convergence of a sequence in multiplicative sense. Corollaries allow this condition to be replaced by multiplicative analogues of Schmidt type slow oscillation condition or Landau type two-sided condition. [ABSTRACT FROM AUTHOR]