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We obtain explicit formulas for the Neumann coefficients and associatedquantities that appear in the three-string vertex for type IIB string theory ina plane-wave background, for any value of the mass parameter mu. The derivationinvolves constructing the inverse of a certain infinite-dimensional matrix, interms of which the Neumann coefficients previously had been written onlyimplicitly. We derive asymptotic expansions for large mu and find unexpectedlysimple results, which are valid to all orders in 1/mu. Using BMN duality, thesegive predictions for certain gauge theory quantities to all orders in themodified 't Hooft coupling lambda'. A specific example is presented.Comment: 28 pages, 2 figures, v2: reference added, new comments and appendix,  typos fixed in eqs. (86) and (89

Explicit formulas for Neumann coefficients in the plane-wave geometry