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Date: 16-4-2019
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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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