Tesseral Harmonic
المؤلف:
Byerly, W. E.
المصدر:
An Elementary Treatise on Fourier,s Series, and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics. New York: Dover
الجزء والصفحة:
...
25-9-2019
1503
Tesseral Harmonic
A tesseral harmonic is a spherical harmonic of the form 
. These harmonics are so named because the curves on which they vanish are 
parallels of latitude and 
meridians, which divide the surface of a sphere into quadrangles whose angles are right angles (Whittaker and Watson 1990, p. 392).
Resolving 
into factors linear in 
, multiplied by 
when 
is odd, then replacing 
by 
allows the tesseral harmonics to be expressed as products of factors linear in 
, 
, and 
multiplied by one of 1, 
, 
, 
, 
, 
, 
, and 
(Whittaker and Watson 1990, p. 536).
REFERENCES:
Byerly, W. E. An Elementary Treatise on Fourier's Series, and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics. New York: Dover, p. 197, 1959.
Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, 1990.
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