Spherical Bessel expansions of sine, cosine, and exponential integrals Original Research Article

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 cos2x, are presented and verified.