{"title":"Index","authors":"","doi":"10.1017/9780511777165.014","DOIUrl":"https://doi.org/10.1017/9780511777165.014","url":null,"abstract":"","PeriodicalId":356498,"journal":{"name":"Encyclopedia of Special Functions: The Askey-Bateman Project","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123342605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Orthogonal Polynomials of Several Variables","authors":"A. Baier","doi":"10.1017/9780511777165.003","DOIUrl":"https://doi.org/10.1017/9780511777165.003","url":null,"abstract":"","PeriodicalId":356498,"journal":{"name":"Encyclopedia of Special Functions: The Askey-Bateman Project","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134227264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Appell and Lauricella Hypergeometric Functions","authors":"K. Matsumoto","doi":"10.1017/9780511777165.004","DOIUrl":"https://doi.org/10.1017/9780511777165.004","url":null,"abstract":"","PeriodicalId":356498,"journal":{"name":"Encyclopedia of Special Functions: The Askey-Bateman Project","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121981972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"General Overview of Multivariable Special Functions","authors":"T. Koornwinder, J. Stokman","doi":"10.1017/9780511777165.002","DOIUrl":"https://doi.org/10.1017/9780511777165.002","url":null,"abstract":"The theory of one-variable (ordinary) hypergeometric and basic hypergeometric series goes back to work of Euler, Gauss and Jacobi. The theory of elliptic hypergeometric series is of a much more recent vintage [20]. The three theories deal with the study of series ∑ k≥0 ck with f (k) := ck+1/ck a rational function in k (hypergeometric theory), a rational function in qk (basic hypergeometric theory), or a doubly periodic meromorphic function in k (elliptic hypergeometric theory, see [21, Ch. 11] for an overview). Examples of elementary functions admitting hypergeometric and basic hypergeometric series representations are","PeriodicalId":356498,"journal":{"name":"Encyclopedia of Special Functions: The Askey-Bateman Project","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130431481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Jacobi Polynomials and Hypergeometric Functions Associated with Root Systems","authors":"G. Heckman, E. Opdam","doi":"10.1017/9780511777165.009","DOIUrl":"https://doi.org/10.1017/9780511777165.009","url":null,"abstract":"","PeriodicalId":356498,"journal":{"name":"Encyclopedia of Special Functions: The Askey-Bateman Project","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122336317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Recursively Defined Polynomials","authors":"","doi":"10.1017/9780511979156.005","DOIUrl":"https://doi.org/10.1017/9780511979156.005","url":null,"abstract":"","PeriodicalId":356498,"journal":{"name":"Encyclopedia of Special Functions: The Askey-Bateman Project","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123276649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Matrix-Valued Orthogonal Polynomials and Differential Equations","authors":"","doi":"10.1017/9780511979156.013","DOIUrl":"https://doi.org/10.1017/9780511979156.013","url":null,"abstract":"","PeriodicalId":356498,"journal":{"name":"Encyclopedia of Special Functions: The Askey-Bateman Project","volume":"105 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114524568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"General Orthogonal Polynomials","authors":"","doi":"10.1017/9780511979156.003","DOIUrl":"https://doi.org/10.1017/9780511979156.003","url":null,"abstract":"","PeriodicalId":356498,"journal":{"name":"Encyclopedia of Special Functions: The Askey-Bateman Project","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133123441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Zeros of Orthogonal Polynomials","authors":"E. Levin, D. Lubinsky","doi":"10.1007/978-1-4613-0201-8_11","DOIUrl":"https://doi.org/10.1007/978-1-4613-0201-8_11","url":null,"abstract":"","PeriodicalId":356498,"journal":{"name":"Encyclopedia of Special Functions: The Askey-Bateman Project","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122262517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Some Families of Matrix-Valued Jacobi Orthogonal Polynomials","authors":"","doi":"10.1017/9780511979156.014","DOIUrl":"https://doi.org/10.1017/9780511979156.014","url":null,"abstract":"","PeriodicalId":356498,"journal":{"name":"Encyclopedia of Special Functions: The Askey-Bateman Project","volume":"172 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122874315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}