T. Ton-That, K. I. Gross, D. St. P. Richards, and P. J. Sally (Eds.) (1995)Representation Theory and Harmonic Analysis.
Contemporary Mathematics, Vol. 191, American Mathematical Society, Providence, RI.
Papers from the conference held in honor of Ray A. Kunze at
the AMS Special Session, Cincinnati, Ohio, January 12–14,
T. M. MacRobert (1967)Spherical Harmonics. An Elementary Treatise on Harmonic Functions with Applications.
3rd edition, International Series of Monographs in Pure and Applied Mathematics, Vol. 98, Pergamon Press, Oxford.
A software package (the successor to CAYLEY) designed to solve
computationally hard problems in algebra, number theory,
geometry, and combinatorics, and to provide a mathematically
rigorous environment for computing with algebraic,
number-theoretic, combinatoric, and geometric objects.
►This release increments the minor version number and contains considerable additions of new material and clarifications.
These additions were facilitated by an extension of the scheme for reference numbers; with “_” introducing intermediate numbers.
These enable insertions of new numbered objects between existing ones without affecting their permanent identifiers and URLs.
In regard to the definition of the spherical
, the domain of the integer originally written
as has been replaced with the more general .
Because of this change, in the sentence just below
(14.30.2), “tesseral for and
sectorial for ” has been replaced with “tesseral for
and sectorial for ”. Furthermore, in
(14.30.4), has been replaced with .
J. C. Adams and P. N. Swarztrauber (1997)SPHEREPACK 2.0: A Model Development Facility.
NCAR Technical NoteTechnical Report TN-436-STR, National Center for Atmospheric Research.
SPHEREPACK 2.0 is a collection of Fortran programs that facilitates
computer modeling of geophysical processes. Accurate solutions are
obtained via the spectral method that uses both scalar and vector
spherical harmonic transforms. The package also contains utility programs
for computing the associated Legendre functions. SPHEREPACK 3.1 was
released in August 2003.
►If is harmonic in , , and for all , then is constant in .
Moreover, if is bounded and is continuous on and harmonic in , then is maximum at some point on .
►Let and be real or complex numbers that are not integers.
►(The integer may be greater than one to allow for a finite number of zero factors.)