A continued fraction approximation of the modified bessel function I1(t)
نویسندگان
چکیده
منابع مشابه
Multidimensional Continued Fraction and Rational Approximation
The classical continued fraction is generalized for studying the rational approximation problem on multi-formal Laurent series in this paper, the construction is called m-continued fraction. It is proved that the approximants of an m-continued fraction converge to a multiformal Laurent series, and are best rational approximations to it; conversely for any multi-formal Laurent series an algorith...
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15 صفحه اولA 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...
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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 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.
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 1990
ISSN: 0893-9659
DOI: 10.1016/0893-9659(90)90037-c