1 Panharmonic Functions Endang Cahya M.A 1 Department of Mathematics, Faculty of Mathematics and Sciences Institut Teknologi Bandung Jl. Ganesa 10, Bandung, 40132-Indonesia Summary In this paper we discuss some properties of panharmonic functions those are similar to harmonic functions. In particular there are generalisations of harmonic functions, Liouville’s theorem, and convergence in the mean theorem. By using Green’s Identity, the uniqueness theorem is shown to produce another generalised harmonic function. Abstrak Tulisan ini membahas beberapa sifat fungsi panharmonik sebagai hasil generalisasi dari sifat fungsi harmonik. Beberapa sifat fungsi panharmonik diperoleh dengan memanfaatkan sifat korespondensi satu-satu antara kelas fungsi panharmonik di bidang dengan sub kelas fungsi harmonik di ruang. Selain itu Ketunggalan fungsi panharmonik dijelaskan dengan memanfaatkan identitas Green. 1. Introduction In this paper we establish some results relating to the solutions of the Yukawa equation, i.e.: u u x u y u 2 2 (1) 2 2 2 , is a positive constant. A C 2 -solution of (1) in a domain 2 is called panharmonic. Equation (1) arose out of an attempt by the Japanese physicist Hideki Yukawa to describe nuclear potential of a point charge as e - r /r. The resulting potential distribution satisfies the 3-dimensional version of equation (1). A comprehensive 1 Permanent address Jurusan Pendidikan Matematika FPMIPA IKIP Bandung