On an Asymptotic Expansion of the Kontorovich–Lebedev Transform

Abstract

An asymptotic expansion valid for large positive values of s is constructed for the integral transform

where denotes the modified Bessel function of purely imaginary order s and the function f(x) is analytic in a suitable sector containing the positive real axis and possesses the asymptotic expansion

as x→ ∞ in this sector, where γ is complex; and .

Keywords:

• Asymptotic expansion
• Integral transform
• Bessel function
• AMS Subject Classification: 41A60
• 44A15
• 33C10