Tesseral Harmonic

A tesseral harmonic is a spherical harmonic of the form cos; sin(mphi)P_l^m(costheta). These harmonics are so named because the curves on which they vanish are l-m parallels of latitude and 2m meridians, which divide the surface of a sphere into quadrangles whose angles are right angles (Whittaker and Watson 1990, p. 392).

Resolving P_l(costheta) into factors linear in cos^2theta, multiplied by costheta when l is odd, then replacing costheta by z/r allows the tesseral harmonics to be expressed as products of factors linear in x^2, y^2, and z^2 multiplied by one of 1, x, y, z, yz, zx, xy, and xyz (Whittaker and Watson 1990, p. 536).

See also

Sectorial Harmonic, Spherical Harmonic, Zonal Harmonic

Explore with Wolfram|Alpha


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.

Referenced on Wolfram|Alpha

Tesseral Harmonic

Cite this as:

Weisstein, Eric W. "Tesseral Harmonic." From MathWorld--A Wolfram Web Resource.

Subject classifications