In mathematics, prolate spheroidal wave functions are eigenfunctions of the Laplacian in prolate spheroidal coordinates, adapted to boundary conditions...

called oblate spheroidal wave functions if oblate spheroidal coordinates are used and prolate spheroidal wave functions if prolate spheroidal coordinates...

product of a radial spheroidal wave function R m n ( − i c , i ξ ) {\displaystyle R_{mn}(-ic,i\xi )} and an angular spheroidal wave function S m n ( − i c ...

equation and wave equation. This could be achieved by expansion of functions in series of trigonometric functions. Whereas the trigonometric functions in a Fourier...

In mathematics, the spheroidal wave equation is given by ( 1 − t 2 ) d 2 y d t 2 − 2 ( b + 1 ) t d y d t + ( c − 4 q t 2 ) y = 0 {\displaystyle (1-t^{2}){\frac...

approximate closely the prolate spheroidal wave functions of order zero. Kaiser, James F. (Nov 1964). "A family of window functions having nearly ideal properties"...

failure of the performance of a task Posterior spinal fusion Prolate spheroidal wave function Pounds per square foot, a measure of pressure; see also Pounds...

corresponding results for Mathieu functions, Lamé functions, prolate spheroidal wave functions, oblate spheroidal wave functions and others). In field theory...

"Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty -- I" (PDF). BSTJ. Retrieved June 15, 2012. "Prolate Spheroidal Wave Functions, Fourier...

"Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions". Bell...

periodic differential equations, as for Lamé functions and prolate and oblate spheroidal wave functions. Mathieu's differential equations appear in a...

Stratton JA, Morse PM, Chu LJ, Hunter RA, Elliptic Cylinder and Spheroidal Wave Functions: Including Tables of Separation Constants and Coefficients, Wiley-MIT...

corresponding calculations for Mathieu functions, and oblate spheroidal wave functions and prolate spheroidal wave functions). With the following boundary conditions...

Dolciani Award in 2020. Slepian, D.; Pollak, H. O. (1961). "Prolate spheroidal wave functions, Fourier analysis and uncertainty. I". The Bell System Technical...

cosine potential (cf. Mathieu function) or other periodic potentials (cf. e.g. Lamé function and spheroidal wave function) and irrespective of whether...

A Maclaurin spheroid is an oblate spheroid which arises when a self-gravitating fluid body of uniform density rotates with a constant angular velocity...

the Slepian functions or discrete prolate spheroidal sequences, after David Slepian (also known in literature as discrete prolate spheroidal sequences or...

mechanics, Meixner polynomials, Meixner–Pollaczek polynomials, and spheroidal wave functions. Meixner began his studies in theoretical physics with Arnold...

Rayleigh waves. Toroidal modes only involve SH waves (like Love waves) and do not exist in fluid outer core. Radial modes are just a subset of spheroidal modes...

Weierstrass Elliptic and Related Functions Parabolic Cylinder Functions Mathieu Functions Spheroidal Wave Functions Orthogonal Polynomials Bernoulli and...

as a wave with field components in transverse polarization (perpendicular to the direction of the wave vector). A mathematical description of wave propagation...

Vaidyanathan, "MIMO radar space-time adaptive processing using prolate spheroidal wave functions", IEEE Transactions on Signal Processing, Feb, 2008. https://ieeexplore...

Stratton JA, Morse PM, Chu LJ, Hunter RA, Elliptic Cylinder and Spheroidal Wave Functions: Including Tables of Separation Constants and Coefficients, Wiley-MIT...

the index ellipsoid; but the principal axes of the spheroidal index ellipsoid and the spheroidal sheet of the index surface are interchanged. In the...

assumption that the secondary waves are spherical for the ordinary refraction (which satisfies Snell's law) and spheroidal for the extraordinary refraction...

(thrómbos) 'clot' and κύτος (kútos) 'cell') are a part of blood whose function (along with the coagulation factors) is to react to bleeding from blood...

related to wave–particle duality. Scattering theory is a framework for studying and understanding the scattering of waves and particles. Wave scattering...

and to the theory of spatiospectral localization via prolate spheroidal wave functions. Simons is involved in the design of marine instrumentation for...

An Airy beam, is a propagation invariant wave whose main intensity lobe propagates along a curved parabolic trajectory while being resilient to perturbations...

Asymptotic expansions of Mathieu functions, spheroidal wave functions, Lamé functions and ellipsoidal wave functions and their eigenvalues. Asymptotic...