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An asymptotic expansion valid for largepositive values of  x  is constructed for the Kontorovich–Lebedev transform   f(x)  = 2/π 2 ∫ 0  ∞  s  sinh( s π) K   is  ( x ) F ( s ) ds  where  K   is  ( x ) denotes the MacDonald type Bessel function of imaginary order. The paper obtains the modifications necessary to an asymptotic expansion of the above transform obtained by Wong (1981) when the latter is inapplicable because certain so called “moments” of the function  F ( s ) sinh( s π) vanish.

On a modification of Wong´s asymptotic expansion of the Kontorovich–Lebedev transform