TY - GEN
T1 - On a version of quaternionic function theory related to mathieu functions
AU - Luna-Elizarrarás, María Elena
AU - Rodríguez-Dagnino, Ramón M.
AU - Shapiro, Michael
PY - 2007
Y1 - 2007
N2 - The angular and radial Mathieu functions, or elliptic-cylinder functions, are solutions of the two ordinary differential equations of the second order with variable coefficients and were originally proposed by È. Mathieu in 1868 for finding the modes in en elliptic membrane. Since then, they have found numerous and important applications to the problems in physics and engineering science thus generating a vast research literature about them. It's appeared recently that there exists a theory of functions with quaternionic values and of two real variables which is determined by a Cauchy-Riemann-type operator with quaternionic, variable coefficients and which is intimately related to the Mathieu equations. In the work, it is explained all the above and some basic facts of the arising quaternionic function theory.
AB - The angular and radial Mathieu functions, or elliptic-cylinder functions, are solutions of the two ordinary differential equations of the second order with variable coefficients and were originally proposed by È. Mathieu in 1868 for finding the modes in en elliptic membrane. Since then, they have found numerous and important applications to the problems in physics and engineering science thus generating a vast research literature about them. It's appeared recently that there exists a theory of functions with quaternionic values and of two real variables which is determined by a Cauchy-Riemann-type operator with quaternionic, variable coefficients and which is intimately related to the Mathieu equations. In the work, it is explained all the above and some basic facts of the arising quaternionic function theory.
KW - Mathieu functions
KW - Quaternionic function theory
KW - Schodinger equation
UR - http://www.scopus.com/inward/record.url?scp=35348886200&partnerID=8YFLogxK
U2 - 10.1063/1.2790264
DO - 10.1063/1.2790264
M3 - Contribución a la conferencia
AN - SCOPUS:35348886200
SN - 073540447X
SN - 9780735404472
T3 - AIP Conference Proceedings
SP - 761
EP - 763
BT - NUMERICAL ANALYSIS AND APPLIED MATHEMATICS
T2 - NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics
Y2 - 16 September 2007 through 20 September 2007
ER -