Ontology type: schema:ScholarlyArticle Open Access: True
2021-06-04
AUTHORS ABSTRACTWe present an explicit formula for the resolvent of the discrete Laplacian on the square lattice, and compute its asymptotic expansions around thresholds in low dimensions. As a by-product we obtain a closed formula for the fundamental solution to the discrete Laplacian. For the proofs we express the resolvent in a general dimension in terms of the Appell–Lauricella hypergeometric function of type C outside a disk encircling the spectrum. In low dimensions it reduces to a generalized hypergeometric function, for which certain transformation formulas are available for the desired expansions. More... »
PAGES32
http://scigraph.springernature.com/pub.10.1007/s00020-021-02648-2
DOIhttp://dx.doi.org/10.1007/s00020-021-02648-2
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