On The Generalized Tricomi's Equation

Year 1968, Volume: 17 , - , 01.01.1968

A. Okay Çelebi

https://doi.org/10.1501/Commua1_0000000588

Abstract

The relation between the 2 - monogenic funetions and the Solutions of the elliptic partial differential equation
8^U dU
dx^
is known [6] ; the ohject of this paper is to investigate the properties of the generalized TricomVs Equation
(*)
8Xj
and its Solutions which will be composed of three sections.
called as S - harmonic fujıctions. Our study is
İn section I we have investigated some properties of the Solutions of the
+
k
+ —
y
= o
n
+
8
U = Q
equation (*).
In section II the well - known Lord Kelvin’s theorem and Almansi’s expan- sion theorem have been established for S-harmonic and S-polyharmonic funetions.
In section III we have proved Brill’s theorem for S - polyharmonic funetions which was previously given for the harmonic funetions.

Keywords

Generalized, Tricomi's Equation, Mathematics

References

• Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi