A tesseral harmonic is a spherical harmonicof 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).