Generalization of two identities in Ramanujan's lost notebook
Generalizations of Milne’s -Chu-Vandermonde summation
We derive two identities for multiple basic hyper-geometric series associated with the unitary group. In order to get the two identities, we first present two known -exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two -Chu-Vandermonde summations established by Milne, we arrive at our...
Generalized Levinson-Durbin sequences and binomial coefficients.
Good lower and upper bounds on binomial coefficients.
Human proofs of identities by Osburn and Schneider.
Hybrid proofs of the -binomial theorem and other identities.
Identities involving reciprocals of binomial coefficients.
Identities of symmetry for Euler polynomials arising from quotients of fermionic integrals invariant under S3.
Improved bounds on the number of ways of expressing as a binomial coefficient.
Integral representations and binomial coefficients.
Integrals and polygamma representations for binomial sums.
Inverse series relations, formal power series and Blodgett-Gessel's type binomial identities.
Jensen proof of a curious binomial identity.
Lacunary formal power series and the Stern-Brocot sequence
Let be a real lacunary formal power series, where εₙ = 0,1 and . It is known that the denominators Qₙ(X) of the convergents of its continued fraction expansion are polynomials with coefficients 0, ±1, and that the number of nonzero terms in Qₙ(X) is the nth term of the Stern-Brocot sequence. We show that replacing the index n by any 2-adic integer ω makes sense. We prove that is a polynomial if and only if ω ∈ ℤ. In all the other cases is an infinite formal power series; we discuss its algebraic...
Le semi-groupe libre des carrés magiques
Nous étudions une loi de composition sur les carrés magiques, qui a déjà été introduite dans la littérature, qui munit l'ensemble de tous les carrés magiques d'une structure de semi-groupe (monoïde). Nous prouvons ensuite une conjecture de Adler et Li, ce semi-groupe est libre.
Lehmer-type congruences for lacunary harmonic sums modulo p²
Linear recurrent sequences and powers of a square matrix.
Mod p³ analogues of theorems of Gauss and Jacobi on binomial coefficients
Modular relations and explicit values of Ramanujan-Selberg continued fractions.
Multiple binomial transforms and families of integer sequences.