PARTIAL SUMS OF GENERALIZED STRUVE FUNCTIONS

Yagmur N., ORHAN H.

MISKOLC MATHEMATICAL NOTES, vol.17, no.1, pp.657-670, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.18514/mmn.2016.1419
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.657-670
  • Keywords: partial sums, analytic functions, generalized Struve functions, Struve and modified Struve functions
  • Ataturk University Affiliated: Yes

Abstract

Let (f(v, d, c))(n) (z) = z + Sigma(n)(k=1) b(k)z(k+1) be the sequence of partial sums of generalized and normalized Struve functions f(v, d, c) (z) = z + Sigma(infinity)(k=1) b(k)z(k+1) where b(k) = (-c/4)(k)/(3/2)(k)(F)(k) and F := v + (d+2)/2 not equal 0, -1, -2, .... The purpose of the present paper is to determine lower bounds for R{f(v, d, c) (z)/(f(v, d, c))(n) (z)}, R{(f(v, d, c))(n) (z)/f(v, d, c) (z)}, R{f'(v, d, c) (z)/(f(v, d, c))'(n) (z)} and R{(f(v, d, c))'(n) (z)/f'(v, d, c) (z)}. Furthermore, we give lower bounds for R{Lambda[f(v, d, c)](z)/Lambda[f(v, d, c)])(n) (z)} and R{Lambda[f(v, d, c)])(n)(z)/Lambda[f(v, d, c)](n) (z)} , where Lambda[f(v, d, c)] the Alexander transform of f(v, d, c).