منابع مشابه
A Specialised Continued Fraction
We display a number with a surprising continued fraction expansion and show that we may explain that expansion as a specialisation of the continued fraction expansion of a formal series: A series ∑ chX −h has a continued fraction expansion with partial quotients polynomials in X of positive degree (other, perhaps than the 0-th partial quotient). Simple arguments, let alone examples, demonstrate...
متن کاملA q-CONTINUED FRACTION
Let a, b, c, d be complex numbers with d 6= 0 and |q| < 1. Define H1(a, b, c, d, q) := 1 1 + −abq + c (a + b)q + d + · · · + −abq + cq (a + b)qn+1 + d + · · · . We show that H1(a, b, c, d, q) converges and 1 H1(a, b, c, d, q) − 1 = c − abq d + aq P∞ j=0 (b/d)(−c/bd)j q (q)j(−aq/d)j P∞ j=0 (b/d)(−c/bd)j q (q)j(−aq/d)j . We then use this result to deduce various corollaries, including the followi...
متن کاملcontinued fraction ∗
We use a continued fraction expansion of the sign-function in order to obtain a five dimensional formulation of the overlap lattice Dirac operator. Within this formulation the inverse of the overlap operator can be calculated by a single Krylov space method where nested conjugate gradient procedures are avoided. We show that the five dimensional linear system can be made well conditioned using ...
متن کاملA Continued Fraction of Ramanujan
In a manuscript discovered in 1976 by George E. Andrews, Ramanujan states a formula for a certain continued fraction, without proof. In this paper we establish formulae for the convergents to the continued fraction, from which Ramanujan's result is easily deduced.
متن کاملOn a continued fraction formula of Wall
We study the combinatorics of a continued fraction formula due to Wall. We also derive the orthogonality of little q-Jacobi polynomials from this formula, as Wall did for little q-Laguerre polynomials.
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 1993
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-1993-058-5