Matrix continued fraction expansion of Bessel function

A CONTINUED FRACTION EXPANSION FOR A q-TANGENT FUNCTION

We prove a continued fraction expansion for a certain q–tangent function that was conjectured by Prodinger.

Continued Fraction Expansions of Matrix Eigenvectors

We examine various properties of the continued fraction expansions of matrix eigenvector slopes of matrices from the SL(2, Z) group. We calculate the average period length, maximum period length, average period sum, maximum period sum and the distributions of 1s 2s and 3s in the periods versus the radius of the Ball within which the matrices are located. We also prove that the periods of contin...

Beta-expansion and continued fraction expansion over formal Laurent series

Let x ∈ I be an irrational element and n 1, where I is the unit disc in the field of formal Laurent series F((X−1)), we denote by kn(x) the number of exact partial quotients in continued fraction expansion of x, given by the first n digits in the β-expansion of x, both expansions are based on F((X−1)). We obtain that lim inf n→+∞ kn(x) n = degβ 2Q∗(x) , lim sup n→+∞ kn(x) n = degβ 2Q∗(x) , wher...

Aggregation Matrix for the Reduced-Order Continued Fraction Expansion Model of Chen and Shieh

where ff = [z‘:w‘],rER and S = i2$<', F=A22-SA12, G = A2,SAU, Ai=[An:A}2\, ~,,ER . Other matrices are compatibly dimensioned. Again it should be noted that the dimension of the partitions in the matrices are not the same as in (1). Equation @I) represents an underdetermined set of (n — m) equations in n unknowns, and thus m entries in each eigenvector corresponding to z-vector can be arbitraril...

A matrix Euclidean algorithm and matrix continued fraction expansions