New series expansion representations for spherical wave functions

New series expansion representations of the normalized functions P-mn(cos t heta) = (P) over bar(n)(\m\)(cos theta), S-mn(cos theta) = (m/sin theta)(P) over bar(n)(\m\)(cos theta), and D-mn(cos theta) = (d/d theta)(P) over bar (n)(\m\)(cos theta) are derived where (P) over bar(n)(\m\)(cos theta) is a new normalized associated Legendre function valid for n > 0, -n less than o r equal to m less than or equal to n, and at 0 less than or equal to theta less than or equal to pi. The usual normalized associated Legendre function (P) over bar(n)(\m\)(cos theta) is valid only for m greater than or equal to 0, and hence is different from (P) over bar(n)(\m\)(cos theta). The deri ved functions are important for applications where vector spherical wave fu nctions are used to analyte the electromagnetic fields. The functions deriv ed here can be computed nonrecursively, and the computation time is of the same order as that using recurrence relations. (C) 2000 John Wiley & Sons, Inc.