Rotational symmetry | Special hypergeometric functions
In the mathematical study of rotational symmetry, the zonal spherical harmonics are special spherical harmonics that are invariant under the rotation through a particular fixed axis. The zonal spherical functions are a broad extension of the notion of zonal spherical harmonics to allow for a more general symmetry group. On the two-dimensional sphere, the unique zonal spherical harmonic of degree ℓ invariant under rotations fixing the north pole is represented in spherical coordinates by where Pℓ is a Legendre polynomial of degree ℓ. The general zonal spherical harmonic of degree ℓ is denoted by , where x is a point on the sphere representing the fixed axis, and y is the variable of the function. This can be obtained by rotation of the basic zonal harmonic In n-dimensional Euclidean space, zonal spherical harmonics are defined as follows. Let x be a point on the (n−1)-sphere. Define to be the dual representation of the linear functional in the finite-dimensional Hilbert space Hℓ of spherical harmonics of degree ℓ. In other words, the following reproducing property holds:for all Y ∈ Hℓ. The integral is taken with respect to the invariant probability measure. (Wikipedia).
Introduction to Cylindrical Coordinates
This video introduces cylindrical coordinates and shows how to convert between cylindrical coordinates and rectangular coordinates. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
Definition of spherical coordinates | Lecture 33 | Vector Calculus for Engineers
We define the relationship between Cartesian coordinates and spherical coordinates; the position vector in spherical coordinates; the volume element in spherical coordinates; the unit vectors; and how to differentiate the spherical coordinate unit vectors. Join me on Coursera: https://www
From playlist Vector Calculus for Engineers
Introduction to Cylindrical Coordinates
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From playlist Calculus 3
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From playlist Workshop on Climate Studies - 2022
Jeffrey Galkowski: Geodesic beams in eigenfunction analysis (part 2 of 2)
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From playlist Geometry
Chris SOGGE - Toponogov's theorem and improved Kakeya-Nikodym estimates...
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From playlist Phys 331 Uploads
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Cylindrical Coordinates to Rectangular Coordinates Example If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Larson Calculus 11.7 Cylindrical and Spherical Coordinates
Semidefinte programming bounds by Abhinav Kumar
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
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Introduction to Spherical Coordinates
This video defines spherical coordinates and explains how to convert between spherical and rectangular coordinates. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
We calculate the functional form of some example spherical harmonics, and discuss their angular dependence.
From playlist Quantum Mechanics Uploads
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Spherical Harmonics and Angular Momentum
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From playlist Quantum Mechanics Uploads
Gergely Harcos - A glimpse at arithmetic quantum chaos
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Spherical Coordinates Check out my Vector Calculus Playlist: https://www.youtube.com/watch?v=1LA8lww1wJg&list=PLJb1qAQIrmmAU22cfpgxqSR5iB7jxh933 Subscribe to my channel: https://www.youtube.com/c/drpeyam
From playlist Double and Triple Integrals
Topologies of the zero sets of random real projective hyper-surfaces... - Peter Sarnak
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3D structure & maintenance of the present day observed Climate (Lecture 1) by B N Goswami
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Introduction to Spherical Coordinates
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From playlist Calculus 3