SOME BOUNDS FOR ALTERNATING MATHIEU TYPE SERIES

Using recent investigated integral representations for the generalized alternating Math- ieu series ˜ S (α,β) μ r; {an} ∞ n=1 r,α,β,μ, {an} ∞ n=1 ∈ R + (9,14,18) with an = nγ, γ ∈ R+ and Mellin-Laplace type integral transforms for the generalized hypergeometric functions and the Bessel function offirstkind, somebounding inequalities for ˜ S (α,β) μ r; {nγ }∞ n=1 are presented. Namely, it is shown that the series ˜ S (α,β) μ r; {nγ }∞ n=1 under some conditions for parameters α, β, γ and μ are bounded with constants which do not depend on α ,β and γ but only depend on r and μ,i.e. ˜ S( α,β) μ r; nγ ∞ n=1 2 (1 + r2)μ .