New theta function identities for a continued fraction of Ramanujan and their applications
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DOI: 10.1007/s13370-020-00823-z
Abstract: We prove three new theta function identities for the continued fraction H ( q ) defined by $$\begin{aligned} H(q):=q^{1/8}-\frac{q^{7/8}}{1-q}_{+}\frac{q^2}{1+q^2}_{-}\frac{q^3}{1-q^3}_{+}\frac{q^4}{1+q^4}_{- \cdots }, \vert q\vert read more here.
Keywords: function identities; theta function; continued fraction; new theta ... See more keywords
Pfaffian formulas and Schur Q-function identities
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DOI: 10.1016/j.aim.2019.07.006
Abstract: We establish Pfaffian analogues of the Cauchy--Binet formula and the Ishikawa--Wakayama minor-summation formula. Each of these Pfaffian analogues expresses a sum of products of subpfaffians of two skew-symmetric matrices in terms of a single Pfaffian.… read more here.
Keywords: formulas schur; function identities; pfaffian formulas; schur function ... See more keywords