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harmonic series definitions

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Merriam Webster's

noun Date: 1866 a series of the form 1 + 1/2^? + 1/3^? + 1/4^? + ... which diverges for 0 ? ? ? 1 and converges for ? > 1

Webster's 1913 Dictionary

the motion of the point A, of the foot of the perpendicular PA, when P moves uniformly in the circumference of a circle, and PA is drawn perpendicularly upon a fixed diameter of the circle. This is simple harmonic motion. The combinations, in any way, of two more simple harmonic motions, make other kinds of harmonic motion. The motion of the pendulum bob of a clock is approximately simple harmonic motion. Harmonic proportion. See under Proportion. Harmonic series or progression. See under Progression. Spherical harmonic analysis, a mathematical method, sometimes referred to as that of Laplace's Coefficients, which has for its object the expression of an arbitrary, periodic function of two independent variables, in the proper form for a large class of physical problems, involving arbitrary data, over a spherical surface, and the deduction of solutions for every point of space. The functions employed in this method are called spherical harmonic functions. --Thomson & Tait. Harmonic suture (Anat.), an articulation by simple apposition of comparatively smooth surfaces or edges, as between the two superior maxillary bones in man; -- called also harmonic, and harmony. Harmonic triad (Mus.), the chord of a note with its third and fifth; the common chord.