Spherical Bessel Expansions of Sine, Cosine, and Exponential Integrals

Frank E. Harris

Department of Physics, University of Utah
Quantum Theory Project, University of Florida

Applied Numerical Math. 34, 95-98 (2000)

   The exponential integral occurs in many physical problems and is  relatively cumbersome to evaluate for an intermediate range of its argument.  It would be helpful to expand that integral as a quadratic series in spherical Bessel functions, but the mathematics literature contains no expansions of this type parallel to the well-known such expansion of the sine integral.  The missing expansion, and an analogous expansion of cos 2x, are presented and verified.