12,447 research outputs found
Polynomial sequences on quadratic curves
In this paper we generalize the study of Matiyasevich on integer points over
conics, introducing the more general concept of radical points. With this
generalization we are able to solve in positive integers some Diophantine
equations, relating these solutions by means of particular linear recurrence
sequences. We point out interesting relationships between these sequences and
known sequences in OEIS. We finally show connections between these sequences
and Chebyshev and Morgan-Voyce polynomials, finding new identities
Note on Ward-Horadam H(x) - binomials' recurrences and related interpretations, II
We deliver here second new recurrence formula,
were array is appointed by sequence of
functions which in predominantly considered cases where chosen to be
polynomials . Secondly, we supply a review of selected related combinatorial
interpretations of generalized binomial coefficients. We then propose also a
kind of transfer of interpretation of coefficients onto
coefficients interpretations thus bringing us back to
and Donald Ervin Knuth relevant investigation decades
ago.Comment: 57 pages, 8 figure
Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order
We employ computer algebra algorithms to prove a collection of identities
involving Bessel functions with half-integer orders and other special
functions. These identities appear in the famous Handbook of Mathematical
Functions, as well as in its successor, the DLMF, but their proofs were lost.
We use generating functions and symbolic summation techniques to produce new
proofs for them.Comment: Final version, some typos were corrected. 21 pages, uses svmult.cl
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