MMN-1419
Partial sums of generalized Struve functions
Abstract
Let (f_{v,d,c})_{n}(z)=z+∑_{k=1}ⁿb_{k}z^{k+1} be the sequence of partial sums of generalized and normalized Struve functions f_{v,d,c}(z)=z+∑_{k=1}^{∞}b_{k}z^{k+1} where b_{k}=(((-c/4)^{k})/((3/2)_{k}(Ϝ)_{k})) and Ϝ:=v+(d+2)/2≠0,-1,-2,.... The purpose of the present paper is to determine lower bounds for Re{((f_{v,d,c}(z))/((f_{v,d,c})_{n}(z)))}, Re{(((f_{v,d,c})_{n}(z))/(f_{v,d,c}(z)))}, Re{((f_{v,d,c}′(z))/((f_{v,d,c})_{n}′(z)))} and Re{(((f_{v,d,c})_{n}′(z))/(f_{v,d,c}′(z)))}. Furthermore, we give lower bounds for Re{((Λ[f_{v,d,c}](z))/((Λ[f_{v,d,c}])_{n}(z)))} and Re{(((Λ[f_{v,d,c}])_{n}(z))/(Λ[f_{v,d,c}](z)))}, where Λ[f_{v,d,c}] is the Alexander transform of f_{v,d,c}.
Vol. 17 (2016), No. 1, pp. 657-670
DOI: 10.18514/MMN.2016.1419