A new integral transform basis function

A new integral transform function:\documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm exp }\left({{\rm - }\zeta {\rm r}} \right)\int_0^\infty {s(n)r^n dn} $$\end{document} where s ( n ) is a positive definite shape function, is proposed and investigated. A test on H   2 +shows that it does not suffer from the inadequacies of earlier integral transform functions, of the form:\documentclass{article}\pagestyle{empty}\begin{document}$$ r^n \int_0^\infty {c(\zeta ){\rm exp}({{-}\xi r})d\zeta } $$\end{document} where c (ζ) is a positive definite shape function.