Spherical harmonic analysis

Spherical harmonic analysis
Spherical Spher"ic*al, Spheric Spher"ic, a. [L. sphaericus, Gr. ???: cf. F. sph['e]rique.] 1. Having the form of a sphere; like a sphere; globular; orbicular; as, a spherical body. [1913 Webster]

2. Of or pertaining to a sphere. [1913 Webster]

3. Of or pertaining to the heavenly orbs, or to the sphere or spheres in which, according to ancient astronomy and astrology, they were set. [1913 Webster]

Knaves, thieves, and treachers by spherical predominance. --Shak. [1913 Webster]

Though the stars were suns, and overburned Their spheric limitations. --Mrs. Browning. [1913 Webster]

{Spherical angle}, {Spherical co["o]rdinate}, {Spherical excess}, etc. See under {Angle}, {Coordinate}, etc.

{Spherical geometry}, that branch of geometry which treats of spherical magnitudes; the doctrine of the sphere, especially of the circles described on its surface.

{Spherical harmonic analysis}. See under {Harmonic}, a.

{Spherical lune},portion of the surface of a sphere included between two great semicircles having a common diameter.

{Spherical opening}, the magnitude of a solid angle. It is measured by the portion within the solid angle of the surface of any sphere whose center is the angular point.

{Spherical polygon},portion of the surface of a sphere bounded by the arcs of three or more great circles.

{Spherical projection}, the projection of the circles of the sphere upon a plane. See {Projection}.

{Spherical sector}. See under {Sector}.

{Spherical segment}, the segment of a sphere. See under {Segment}.

{Spherical triangle},re on the surface of a sphere, bounded by the arcs of three great circles which intersect each other.

{Spherical trigonometry}. See {Trigonometry}. [1913 Webster] -- {Spher"ic*al*ly}, adv. -- {Spher"ic*al*ness}, n. [1913 Webster]


The Collaborative International Dictionary of English. 2000.

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  • Spherical harmonic analysis — Harmonic Har*mon ic (h[aum]r*m[o^]n [i^]k), Harmonical Har*mon ic*al ( [i^]*kal), a. [L. harmonicus, Gr. armoniko s; cf. F. harmonique. See {Harmony}.] 1. Concordant; musical; consonant; as, harmonic sounds. [1913 Webster] Harmonic twang! of… …   The Collaborative International Dictionary of English

  • Harmonic analysis — is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms. The basic waves are called harmonics… …   Wikipedia

  • Noncommutative harmonic analysis — In mathematics, noncommutative harmonic analysis is the field in which results from Fourier analysis are extended to topological groups which are not commutative. Since for locally compact abelian groups have a well understood theory, Pontryagin… …   Wikipedia

  • Harmonic — Har*mon ic (h[aum]r*m[o^]n [i^]k), Harmonical Har*mon ic*al ( [i^]*kal), a. [L. harmonicus, Gr. armoniko s; cf. F. harmonique. See {Harmony}.] 1. Concordant; musical; consonant; as, harmonic sounds. [1913 Webster] Harmonic twang! of leather, horn …   The Collaborative International Dictionary of English

  • Harmonic interval — Harmonic Har*mon ic (h[aum]r*m[o^]n [i^]k), Harmonical Har*mon ic*al ( [i^]*kal), a. [L. harmonicus, Gr. armoniko s; cf. F. harmonique. See {Harmony}.] 1. Concordant; musical; consonant; as, harmonic sounds. [1913 Webster] Harmonic twang! of… …   The Collaborative International Dictionary of English

  • Harmonic motion — Harmonic Har*mon ic (h[aum]r*m[o^]n [i^]k), Harmonical Har*mon ic*al ( [i^]*kal), a. [L. harmonicus, Gr. armoniko s; cf. F. harmonique. See {Harmony}.] 1. Concordant; musical; consonant; as, harmonic sounds. [1913 Webster] Harmonic twang! of… …   The Collaborative International Dictionary of English

  • Harmonic progression — Harmonic Har*mon ic (h[aum]r*m[o^]n [i^]k), Harmonical Har*mon ic*al ( [i^]*kal), a. [L. harmonicus, Gr. armoniko s; cf. F. harmonique. See {Harmony}.] 1. Concordant; musical; consonant; as, harmonic sounds. [1913 Webster] Harmonic twang! of… …   The Collaborative International Dictionary of English

  • Harmonic proportion — Harmonic Har*mon ic (h[aum]r*m[o^]n [i^]k), Harmonical Har*mon ic*al ( [i^]*kal), a. [L. harmonicus, Gr. armoniko s; cf. F. harmonique. See {Harmony}.] 1. Concordant; musical; consonant; as, harmonic sounds. [1913 Webster] Harmonic twang! of… …   The Collaborative International Dictionary of English

  • Harmonic series — Harmonic Har*mon ic (h[aum]r*m[o^]n [i^]k), Harmonical Har*mon ic*al ( [i^]*kal), a. [L. harmonicus, Gr. armoniko s; cf. F. harmonique. See {Harmony}.] 1. Concordant; musical; consonant; as, harmonic sounds. [1913 Webster] Harmonic twang! of… …   The Collaborative International Dictionary of English

  • Harmonic suture — Harmonic Har*mon ic (h[aum]r*m[o^]n [i^]k), Harmonical Har*mon ic*al ( [i^]*kal), a. [L. harmonicus, Gr. armoniko s; cf. F. harmonique. See {Harmony}.] 1. Concordant; musical; consonant; as, harmonic sounds. [1913 Webster] Harmonic twang! of… …   The Collaborative International Dictionary of English

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