Ramanujan's Master Theorem and two formulas for zero-order Hankel transform
Abstract
Using Ramanujan's Master Theorem, two formulas are derived which define the Hankel transforms of order zero with even functions by inverse Mellin transforms, provided these functions and their derivatives obey special conditions. Their validity is illustrated by a number of examples. With a help of one of these formulas, one as yet unknown parametric improper integral of the Bessel function J0(x) is calculated.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.