Addition theorems for B functions and other exponentially declining functions

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Abstract
In this paper addition theorems are derived for a special class of exponentially declining functions, the so‐called B functions Bmn,l (α,r) [E. Filter and E. O. Steinborn, Phys. Rev. A 1 8, 1 (1978)]. Although these B functions have a relatively complicated analytical structure they nevertheless have some mathematical properties that are particularly advantageous in connection with multicenter problems. Also, all the commonly occurring exponentially declining functions like, for instance, bound‐state hydrogen eigenfunctions and Slater‐type functions, can be expressed by simple finite sums of B functions. Consequently, addition theorems for these functions can also be written down immediately. The various addition theorems for B functions are derived by applying suitable generating differential operators to the well‐known addition theorem of the special B function Bm−l,l, which is that solution of the modified Helmholtz equation that is irregular at the origin and regular at infinity [E. J. Weniger and E. O. Steinborn, J. Math. Phys. 2 6, 664 (1985)]. All differentiations, which have to be done in this approach, can be expressed in closed form leading to comparatively compact addition theorems.