Representation with majorant of the Schwarz lemma at the boundary
نویسندگان
چکیده
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so that d(r, 0; ƒ') is the length of the segment on the w-plane between the image of the point 3 = 0 and the image of the point z = re. The lemma of Schwarz is the following: THEOREM 1. Let w=f(z) be analytic f or \z\ < 1 . If d(r,6;f)S 1 for all (r, 6) with r<l, then (1) d(r,0;f)gr and (2) | / ( 0 ) | ^ 1 . The sign of equality holds in (1) (for r^O) and in (2), if and only if \f(z) | = 1 ; th...
متن کاملdeterminant of the hankel matrix with binomial entries
abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.
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ژورنال
عنوان ژورنال: Publications de l'Institut Mathematique
سال: 2017
ISSN: 0350-1302,1820-7405
DOI: 10.2298/pim1715191o