Add to ORKGI revisit Bressoud's generalised Borwein conjecture. Making use of certain positivity-preserving transformations for q-binomial coefficients, I establish the truth of infinitely many new cases of the Bressoud conjecture. In addition, I prove new doubly-bounded refinement of the Foda-Quano identities. Finally, I discuss new companions to the Bressoud even moduli identities. In particular, all 10 mod 20 identities are derived.Comment: 14 page
AbstractIt is known that∑k=0∞(2kk)(2k+1)4k=π2and∑k=0∞(2kk)(2k+1)16k=π3. In this paper we obtain thei...
AbstractRecently, R. Tauraso established finite p-analogues of Apéryʼs famous series for ζ(2) and ζ(...
In this paper, we showed some generalized refinements and reverses of arithmetic-geometric-harmonic ...
We consider some finite binomial sums involving the derivatives of the binomial coefficient and deve...
Around 2004, J. Lovejoy proved three Hecke-type series identities using Bailey pairs. In this articl...
summary:In this note, we estimate the distance between two $q$-nomial coefficients $\bigl \lvert \bi...
In this paper, we deduce several new identities on infinite series with denominators of summands con...
summary:Some generalizations of the Ostrowski inequality, the Milovanović-Pečarić-Fink inequality, t...
summary:The main purpose of this paper is to study the mean value properties of a sum analogous to c...
AbstractIn this paper, we prove a new identity for the product of two partial theta functions. An im...
2000 Mathematics Subject Classification: 33D60, 26A33, 33C60The present paper envisages the applicat...
We discuss the properties of the Hankel transformation of a sequence whose elements are the sums of ...
AbstractRamanujan recorded additive formulae of theta functions that are related to modular equation...
By introducing multi-parameters and conjugate exponents and using Euler-Maclaurin’s summation formul...
* The second author is supported by the Alexander-von-Humboldt Foundation. He is on leave from: Inst...
AbstractIt is known that∑k=0∞(2kk)(2k+1)4k=π2and∑k=0∞(2kk)(2k+1)16k=π3. In this paper we obtain thei...
AbstractRecently, R. Tauraso established finite p-analogues of Apéryʼs famous series for ζ(2) and ζ(...
In this paper, we showed some generalized refinements and reverses of arithmetic-geometric-harmonic ...
We consider some finite binomial sums involving the derivatives of the binomial coefficient and deve...
Around 2004, J. Lovejoy proved three Hecke-type series identities using Bailey pairs. In this articl...
summary:In this note, we estimate the distance between two $q$-nomial coefficients $\bigl \lvert \bi...
In this paper, we deduce several new identities on infinite series with denominators of summands con...
summary:Some generalizations of the Ostrowski inequality, the Milovanović-Pečarić-Fink inequality, t...
summary:The main purpose of this paper is to study the mean value properties of a sum analogous to c...
AbstractIn this paper, we prove a new identity for the product of two partial theta functions. An im...
2000 Mathematics Subject Classification: 33D60, 26A33, 33C60The present paper envisages the applicat...
We discuss the properties of the Hankel transformation of a sequence whose elements are the sums of ...
AbstractRamanujan recorded additive formulae of theta functions that are related to modular equation...
By introducing multi-parameters and conjugate exponents and using Euler-Maclaurin’s summation formul...
* The second author is supported by the Alexander-von-Humboldt Foundation. He is on leave from: Inst...
AbstractIt is known that∑k=0∞(2kk)(2k+1)4k=π2and∑k=0∞(2kk)(2k+1)16k=π3. In this paper we obtain thei...
AbstractRecently, R. Tauraso established finite p-analogues of Apéryʼs famous series for ζ(2) and ζ(...
In this paper, we showed some generalized refinements and reverses of arithmetic-geometric-harmonic ...