1988
DOI: 10.1016/0021-9045(88)90087-1
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Equiconvergence of some sequences of complex interpolating rational functions

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Cited by 3 publications
(3 citation statements)
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“…We select p = 6 and (<x, m)= (2,8). The three figures corresponding to «= 10,15,21 show that the Taylor polynomial S n {z,f 8 ) has a zero of order 8 at z o =0 and its remaining (n -8) zeros are distributed on the circle \z\ = 6.…”
Section: Discussion Of Numerical Resultsmentioning
confidence: 99%
“…We select p = 6 and (<x, m)= (2,8). The three figures corresponding to «= 10,15,21 show that the Taylor polynomial S n {z,f 8 ) has a zero of order 8 at z o =0 and its remaining (n -8) zeros are distributed on the circle \z\ = 6.…”
Section: Discussion Of Numerical Resultsmentioning
confidence: 99%
“…, £ -1. j=o It may be noted that a classical theorem of Walsh ([9] p.153) which deals with equiconvergence of certain sequences of polynomials is a special case for each of the results (1.5) -(1.7). For further information on this topic we refer the interested reader to [1,3,7].…”
Section: Introductionmentioning
confidence: 99%
“…For \t\ > 1 and a > 1 tie following identity holds: It is easy to see the validity of the following expansion:If we let 5(3, A) = ( A «+_T 2 ) ( ( -^-n ) ' " 1 ) / ( ( t ' t " ^" n ) A ' + '~1) i° equation (3.1), then (3.2) follows immediately from (3.4) on observing that Now we define another sequence of help functions. Let m+n(3)(4)(5) r; +m , n (z, / , u) := £ c)iy)z*/(z n -a n ), v = i ^)^v \ »"/ •£{-i\ J j J*** * F or i/ = 0, we set be K+ m , n i z , f, 0) = r n+m>n (z, f).On using (1.3), an integral representation of r * + m n ( z , / , u), u ^ 1, is found to . n (*, /, ") = JL^y g Mt, , m t, g…”
mentioning
confidence: 99%