Difference equations and Omega functions
Abstract
We introduce Omega functions that generalize Euler Gamma functions and study the functional difference equation they satisfy. Under a natural exponential growth condition, the vector space of meromorphic solutions of the functional equation is finite dimensional. We construct a basis of the space of solutions composed by Omega functions. Omega functions are defined as exponential periods. They have a meromorphic extension to the complex plane of order 1 with simple poles at negative integers. The vector space they span is characterized by their functional equation and their growth property on vertical strips. This generalizes Wielandt's characterization of Euler Gamma function. We also introduce Incomplete Omega functions that play an important role in the proofs.
Read the paper
Related studies
- eggNOG 5.0: a hierarchical, functionally and phylogenetically annotated orthology resource based on 5090 organisms and 2502 viruses
- Online Survival Analysis Software to Assess the Prognostic Value of Biomarkers Using Transcriptomic Data in Non-Small-Cell Lung Cancer
- OptiType: precision HLA typing from next-generation sequencing data
- Nicotinic Cholinergic System and COVID-19: In Silico Identification of an Interaction between SARS-CoV-2 and Nicotinic Receptors with Potential Therapeutic Targeting Implications
- Saccharomyces cerevisiae cells have three Omega class glutathione S-transferases acting as 1-Cys thiol transferases
- Hemolysis at low blood flow rates: in-vitro and in-silico evaluation of a centrifugal blood pump
Go deeper in Evidence Hub
Evidence Hub adds a study data sheet (design, sample size, evidence level, key numbers), an AI summary and a chat grounded in the paper's text.