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Some theta-function identities
Applied Mathematics and Computation, 2007Using an identity obtained in an earlier paper [\textit{B. Srivastava}, Kyungpook Math. J. 45, 603--607 (2005; Zbl 1101.11005)] the author derives new theta-function identities. One of these leads to another proof of the classical formula for the number of representations of a positive integer as a sum of two squares.
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Various partition function identities
Ars Comb., 2000N. Robbins proves seven integer partitions identities. We give two of them. If \(p(n)\), \(q(n)\), and \(q_0(n)\) denote the numbers of unrestricted partitions, partitions into distinct parts, and partitions into distinct odd parts, and \(t(n)=n(n+1)/2\) are triangular numbers, then \[ \sum _{j=0}^nq_0(n-j)q_0(j)=p(n/2)+2\sum _{j\geq 1}p((n-j^2)/2 ...
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On a functional identity involving inverses on matrix rings
Quaestiones Mathematicae, 2023Wu Jing
exaly
Ecto-ATPases: Identities and Functions
1995Ecto-ATPases are ubiquitous in eukaryotic cells. They hydrolyze extracellular nucleoside tri- and/or diphosphates, and, when isolated, they exhibit E-type ATPase activity, (that is, the activity is dependent on Ca2+ or Mg2+, and it is insensitive to specific inhibitors of P-type, F-type, and V-type ATPases; in addition, several nucleotide tri- and/or ...
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