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dc.format.extent115108 bytes
dc.rightsUrheberrechtlich geschützt
dc.subjectHypergeometrische Reiheger
dc.subjectBieberbach conjectureeng
dc.subjectde Branges functionseng
dc.subjectWeinstein functionseng
dc.subjecthypergeometric functionseng
dc.titleSolution properties of the de Branges differential recurrence equationeng
dcterms.abstractIn this 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums thas was published by Askey and Gasper in 1976. The de Branges functions Tn/k(t) are defined as the solutions of a system of differential recurrence equations with suitably given initial values. The essential fact used in the proof of the Bieberbach and Milin conjectures is the statement Tn/k(t)<=0. In 1991 Weinstein presented another proof of the Bieberbach and Milin conjectures, also using a special function system Λn/k(t) which (by Todorov and Wilf) was realized to be directly connected with de Branges', Tn/k(t)=-kΛn/k(t), and the positivity results in both proofs Tn/k(t)<=0 are essentially the same. In this paper we study differential recurrence equations equivalent to de Branges' original ones and show that many solutions of these differential recurrence equations don't change sign so that the above inequality is not as surprising as expected. Furthermore, we present a multiparameterized hypergeometric family of solutions of the de Branges differential recurrence equations showing that solutions are not rare at all.eng
dcterms.accessRightsopen access
dcterms.creatorKoepf, Wolfram
dcterms.creatorSchmersau, Dieter
dcterms.isPartOfMathematische Schriften Kassel ;; 05, 18ger
dcterms.source.journalMathematische Schriften Kasselger
dcterms.source.volume05, 18

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