International Journal of Pure and Applied Mathematics Volume 85 No. 1 2013, 13-22 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v85i1.2 P A ijpam.eu ON SYSTEMATIC GENERATION OF BIHARMONIC FUNCTIONS Nkem Ogbonna Department of Mathematics Michael Okpara University of Agriculture Umudike, Abia State, NIGERIA Abstract: We present some results for systematic generation of biharmonic functions that are not readily obtainable by a direct application of the sepa- ration of variable technique to the biharmonic equation. Almansi’s theorem and the Kelvin transformation were adapted to obtain the results, and they are presented as theorems followed by simple proofs. The results are not only labour-saving, but also have important implications for the construction of so- lutions to boundary value problems involving composite media with curved geometry. AMS Subject Classification: 31B30 Key Words: systematic generation, harmonic, biharmonic functions, Al- mansi’s theorem, Kelvin transformation 1. Introduction The biharmonic equation ∇ 4 Φ=0, (1) where ∇ is the del operator, has applications in many areas of continuum mechanics. For example, in solid mechanics, it is used to model elasto-static deformation in the absence of body forces and its solution Φ may represent Received: May 11, 2012 c  2013 Academic Publications, Ltd. url: www.acadpubl.eu