On the irrationality of \(\sum \frac{t^n} {A\alpha^n+ B\beta^n}\)
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Publication:1277174
DOI10.1006/jnth.1998.2304zbMath0920.11044OpenAlexW2050706497MaRDI QIDQ1277174
Publication date: 21 June 1999
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jnth.1998.2304
Padé approximationimaginary quadratic number fieldsirrationalitymeromorphic functionsbinary linear recurring sequencemeasures of irrational
Padé approximation (41A21) Measures of irrationality and of transcendence (11J82) Irrationality; linear independence over a field (11J72)
Related Items (5)
Quantitative irrationality for sums of reciprocals of Fibonacci and Lucas numbers ⋮ Linear independence results for sums of reciprocals of Fibonacci and Lucas numbers ⋮ Summation of certain infinite Lucas-related series ⋮ Diophantine approximations using Padé approximations ⋮ Irrationality measures for the series of reciprocals from recurrence sequences.
Cites Work
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- On the linear independence of the values of polylogarithmic functions
- Convergence of Padé approximants of partial theta functions and the Rogers-Szegö polynomials
- An asymptotic formula for \(\pi\)
- Irrationalité de certaines intégrales hypergéométriques. (Irrationality of certain hypergeometric integrals)
- Polynômes orthogonaux formels - applications
- Rate of convergence of Padé approximants for a particular Wynn series
- Convergence of Padé approximants for a \(q\)-hypergeometric series (Wynn's power series III)
- On the irrationality of \(\sum (1/(q^ n+r))\)
- Approximants de Padé et $U$-dérivation
- A New Formula for π
- A GENERAL SYSTEM OF ORTHOGONAL POLYNOMIALS
- On the irrationality of certain series
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