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# 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).

Sectorial Harmonic, Spherical Harmonic, Zonal Harmonic

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## 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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Tesseral Harmonic

## Cite this as:

Weisstein, Eric W. "Tesseral Harmonic." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TesseralHarmonic.html