{"id":"https://openalex.org/W7224097547","doi":"https://doi.org/10.48550/arxiv.2610.36409","title":"Moment representations for generalized Lehmer polynomials","display_name":"Moment representations for generalized Lehmer polynomials","publication_year":2026,"publication_date":"2026-10-26","ids":{"openalex":"https://openalex.org/W7224097547","doi":"https://doi.org/10.48550/arxiv.2610.36409"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.36409","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.36409","pdf_url":"https://arxiv.org/pdf/2610.36409","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.36409","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011289294","display_name":"Karin Ikeda","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ikeda, Karin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5079822882","display_name":"Hideki Murahara","orcid":"https://orcid.org/0000-0002-4176-0407","observed_orcids":["https://orcid.org/0000-0002-4176-0407"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Murahara, Hideki","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.86080002784729,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.86080002784729,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.11129999905824661,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.01119999960064888,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/moment-representation","display_name":"moment representation","score":0.878000020980835},{"id":"https://openalex.org/keywords/negative-binomial-distribution","display_name":"negative binomial distribution","score":0.8700000047683716},{"id":"https://openalex.org/keywords/exponential-generating-functions","display_name":"exponential generating functions","score":0.7559999823570251},{"id":"https://openalex.org/keywords/eulerian-polynomials","display_name":"Eulerian polynomials","score":0.8410000205039978},{"id":"https://openalex.org/keywords/poly-bernoulli-numbers","display_name":"poly-Bernoulli numbers","score":0.9900000095367432},{"id":"https://openalex.org/keywords/log-convexity","display_name":"log-convexity","score":0.9570000171661377},{"id":"https://openalex.org/keywords/boundary-distributions","display_name":"boundary distributions","score":0.7670000195503235}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8877999782562256},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5644000172615051},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.5550000071525574},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.51910001039505},{"id":"https://openalex.org/C4285052","wikidata":"https://www.wikidata.org/wiki/Q3406268","display_name":"Moment problem","level":3,"score":0.49300000071525574},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.490200012922287},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4542999863624573},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.44449999928474426},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44179999828338623},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.42489999532699585},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.423799991607666},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4221999943256378},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.41620001196861267},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.38109999895095825},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37439998984336853},{"id":"https://openalex.org/C167211080","wikidata":"https://www.wikidata.org/wiki/Q285771","display_name":"Riemann\u2013Stieltjes integral","level":3,"score":0.3646000027656555},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.3544999957084656},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3508000075817108},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.34869998693466187},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.322299987077713},{"id":"https://openalex.org/C180099792","wikidata":"https://www.wikidata.org/wiki/Q26708","display_name":"Binomial theorem","level":2,"score":0.3215000033378601},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32019999623298645},{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.31769999861717224},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C101796028","wikidata":"https://www.wikidata.org/wiki/Q535587","display_name":"Moment-generating function","level":3,"score":0.2969000041484833},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.2939000129699707},{"id":"https://openalex.org/C139505817","wikidata":"https://www.wikidata.org/wiki/Q5527834","display_name":"Gaussian binomial coefficient","level":4,"score":0.2924000024795532},{"id":"https://openalex.org/C118733216","wikidata":"https://www.wikidata.org/wiki/Q332504","display_name":"Absolute continuity","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.289900004863739},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2888000011444092},{"id":"https://openalex.org/C61062188","wikidata":"https://www.wikidata.org/wiki/Q835065","display_name":"Second moment of area","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C54865166","wikidata":"https://www.wikidata.org/wiki/Q844937","display_name":"Multiple integral","level":2,"score":0.27489998936653137},{"id":"https://openalex.org/C118431652","wikidata":"https://www.wikidata.org/wiki/Q17098827","display_name":"Mehler\u2013Heine formula","level":5,"score":0.2720000147819519},{"id":"https://openalex.org/C149717495","wikidata":"https://www.wikidata.org/wiki/Q117806","display_name":"Gamma distribution","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C85384003","wikidata":"https://www.wikidata.org/wiki/Q5421525","display_name":"Exponential polynomial","level":3,"score":0.26010000705718994},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.25839999318122864},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.2556000053882599},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2542000114917755},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.36409","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.36409","pdf_url":"https://arxiv.org/pdf/2610.36409","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.36409","doi":"https://doi.org/10.48550/arxiv.2610.36409","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.36409","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.36409","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.36409","pdf_url":"https://arxiv.org/pdf/2610.36409","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224097547.pdf","grobid_xml":"https://content.openalex.org/works/W7224097547.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2794927221","https://openalex.org/W7141629778"],"related_works":["https://openalex.org/W2044899044","https://openalex.org/W2013900951","https://openalex.org/W2558879285","https://openalex.org/W2005927284","https://openalex.org/W7077909677","https://openalex.org/W4299611228","https://openalex.org/W7077083825","https://openalex.org/W3111285862","https://openalex.org/W7101433119","https://openalex.org/W3008542919"],"abstract_inverted_index":{"We":[0,42,58],"represent":[1],"normalized":[2],"generalized":[3],"Lehmer":[4],"polynomials":[5],"as":[6],"moments":[7],"of":[8,27,35,52,55],"a":[9,49],"random":[10],"variable":[11],"constructed":[12],"from":[13],"two":[14],"independent":[15,21],"negative":[16],"binomial":[17],"variables":[18],"and":[19,38,47,72,74],"an":[20],"uniform":[22,36],"variable.":[23],"An":[24],"integral":[25],"form":[26],"their":[28],"known":[29],"exponential":[30],"generating":[31],"function":[32],"yields":[33],"mixtures":[34],"distributions":[37],"convergent":[39],"double":[40],"series.":[41],"recover":[43],"Eulerian":[44],"polynomial":[45],"identities":[46],"give":[48],"probabilistic":[50],"interpretation":[51],"anti-diagonal":[53],"sums":[54],"poly-Bernoulli":[56],"numbers.":[57],"also":[59],"prove":[60],"moment":[61],"determinacy,":[62],"characterize":[63],"the":[64,76],"Stieltjes":[65],"parameter":[66],"range,":[67],"derive":[68],"Hankel":[69],"total":[70],"non-negativity":[71],"log-convexity,":[73],"identify":[75],"boundary":[77],"distributions.":[78]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-29T00:00:00"}
