{"arxiv_id":"1105.0508","incoming":{"papers":50,"sentences":187,"groups":[{"kind":"extends","label":"Builds on it","papers":3,"sentences":3,"quotes":[{"arxiv_id":"1210.0207","title":"Confluence of apparent singularities in multi-indexed orthogonal polynomials: the Jacobi case","url":"/paper/1210.0207","section":"Explicit forms of the multi-indexed Jacobi polynomials","sentence":"With a slight change of notation, these formulas are generalisation of those in [ref] with the inclusion of the type III seed solutions.","intent_p":0.95,"contests_p":null},{"arxiv_id":"1207.5584","title":"Multi-indexed Wilson and Askey-Wilson Polynomials","url":"/paper/1207.5584","section":"Introduction","sentence":"Following the examples of multi-indexed Laguerre and Jacobi polynomials [ref] , multi-indexed ($q$-)Racah polynomials [ref] , we present multi-indexed Wilson and Askey-Wilson polynomials constructed in the framework of discrete quantum mechanics with pure imaginary shifts [ref] 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constructed.","intent_p":0.93,"contests_p":null},{"arxiv_id":"1301.3980","title":"Extensions of solvable potentials with finitely many discrete eigenstates","url":"/paper/1301.3980","section":"Introduction","sentence":"Once the virtual state wavefunctions are identified, the multi-indexed extensions are trivially realised in the manner explained in [ref] .","intent_p":0.82,"contests_p":null},{"arxiv_id":"1612.00927","title":"Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials","url":"/paper/1612.00927","section":"Wronskian forms of the multi-indexed Laguerre and Jacobi polynomials","sentence":"We deform the original Hamiltonian system [ref] by applying multiple Darboux transforma­tions [ref] in terms of $M_$ Type $$ seed solutions and $M_$ Type $$ seed solutions specified by the degree set $𝒟{d_1,…,d_M}$ (ordered set), $MM_+M_$, $M_#{d_j | d_j∈𝒟, Type $$}$, $M_#{d_j | d_j∈𝒟, Type 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deformations.","intent_p":0.87,"contests_p":null},{"arxiv_id":"1612.00927","title":"Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials","url":"/paper/1612.00927","section":"Introduction","sentence":"In the original expressions in [ref] , the matrix elements of the determinants contain the non-polynomial factors, see [ref]–[ref].","intent_p":0.97,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1309.2346","title":"Equivalences of the Multi-Indexed Orthogonal Polynomials","url":"/paper/1309.2346","section":"Zero level deletion","sentence":"If the degree of virtual state wavefunction for deletion is zero ($d_j=0$), an $M$-indexed orthogonal polynomial reduces to an $(M-1)$-indexed orthogonal polynomial [ref] : [equation] which are the consequences of shape-invariance.","intent_p":0.97,"contests_p":null}]},{"kind":"background","label":"Cites it as 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