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On Infinitely Many Rational Approximants to ζ(3)
- Source :
- Mathematics, Volume 7, Issue 12, e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid, instname
- Publication Year :
- 2019
- Publisher :
- MDPI AG., 2019.
-
Abstract
- A set of second order holonomic difference equations was deduced from a set of simultaneous rational approximation problems. Some orthogonal forms involved in the approximation were used to compute the Casorati determinants for its linearly independent solutions. These solutions constitute the numerator and denominator sequences of rational approximants to &zeta<br />( 3 ) . A correspondence from the set of parameters involved in the holonomic difference equation to the set of holonomic bi-sequences formed by these numerators and denominators appears. Infinitely many rational approximants can be generated.
- Subjects :
- Pure mathematics
holonomic difference equation
Differential equation
Matemáticas
General Mathematics
01 natural sciences
Set (abstract data type)
0103 physical sciences
recurrence relation
Computer Science (miscellaneous)
Order (group theory)
Computer Science::Symbolic Computation
Integer Sequences
0101 mathematics
Engineering (miscellaneous)
Mathematics
integer sequences
Recurrence Relation
Orthogonal Forms
Recurrence relation
Holonomic
010102 general mathematics
Integer sequence
Simultaneous Rational Approximation
multiple orthogonal polynomials
Holonomic Difference Equation
Multiple Orthogonal Polynomials
010307 mathematical physics
Linear independence
simultaneous rational approximation
Irrationality
irrationality
orthogonal forms
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Mathematics, Volume 7, Issue 12, e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid, instname
- Accession number :
- edsair.doi.dedup.....c0e5e54c7a3469723ee1cd524e115fce