{"corpus_id":126163900,"paper_sha":"f6f9167843c0521c2c2e895f9cd3bc8ec15d5fe4","doi":"10.1142/S1793042118501737","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":2882994152,"dblp_id":null,"acl_id":null,"title":"On applications for Mahler expansion associated with p-adic q-integrals","year":2019,"publication_date":"2019-02-13","venue":"International Journal of Number Theory","journal":{"name":"International Journal of Number Theory","pages":null,"volume":null},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics"],"reference_count":6,"citation_count":3,"influential_citation_count":0,"is_open_access":false,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"In this paper, we primarily consider a generalization of the fermionic [Formula: see text]-adic [Formula: see text]-integral on [Formula: see text] including the parameters [Formula: see text] and [Formula: see text] and investigate its some basic properties. By means of the foregoing integral, we introduce two generalizations of [Formula: see text]-Changhee polynomials and numbers as [Formula: see text]-Changhee polynomials and numbers with weight [Formula: see text] and [Formula: see text]-Changhee polynomials and numbers of second kind with weight [Formula: see text]. For the mentioned polynomials, we obtain new and interesting relationships and identities including symmetric relation, recurrence relations and correlations associated with the weighted [Formula: see text]-Euler polynomials, [Formula: see text]-Stirling numbers of the second kind and Stirling numbers of first and second kinds. Then, we discover multifarious relationships among the two types of weighted [Formula: see text]-Changhee polynomials and [Formula: see text]-adic gamma function. Also, we compute the weighted fermionic [Formula: see text]-adic [Formula: see text]-integral of the derivative of [Formula: see text]-adic gamma function. Moreover, we give a novel representation for the [Formula: see text]-adic Euler constant by means of the weighted [Formula: see text]-Changhee polynomials and numbers. We finally provide a quirky explicit formula for [Formula: see text]-adic Euler constant.","claims":[{"public_id":"cl_6d2c8b5e38ebed4a49b4b5700ac81ad4","status":"active","text":"A generalized fermionic p-adic q-integral on Z_p is introduced with additional parameters and its basic properties are investigated.","confidence":0.98,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_6d2c8b5e38ebed4a49b4b5700ac81ad4"},{"public_id":"cl_7a4c63699858fb5e92f9c0e18377c57e","status":"active","text":"A new representation for the p-adic Euler constant is given in terms of weighted q-Changhee polynomials and numbers, along with an explicit formula for the p-adic Euler constant.","confidence":0.96,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous 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computed.","confidence":0.95,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_c03c9612f85d62bbb600a860d3d156b9"},{"public_id":"cl_0b10371b24ed4bd5eb21a081ba54cd3c","status":"active","text":"Weighted q-Changhee polynomials and numbers, together with q-Changhee polynomials and numbers of second kind with weight u, are introduced as two generalizations derived from the integral.","confidence":0.97,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_0b10371b24ed4bd5eb21a081ba54cd3c"}],"concepts":[{"public_id":"co_21470f332c9579268e0f334bdd5023bb","status":"active","name":"Stirling numbers of the second kind","description":"Combinatorial numbers counting partitions of a set into nonempty unlabeled 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