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...

applied mathematics, oblate spheroidal wave functions (like also prolate spheroidal wave functions and other related functions) are involved in the solution...

S(t):=(1-t^{2})^{b/2}y(t)} , then S ( t ) {\displaystyle S(t)} is a prolate spheroidal wave function in the sense that it satisfies the equation ( 1 − t 2 ) d 2...

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...

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

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

Cambridge: Cambridge University Press, 1993. Slepian, D. (1978) "Prolate spheroidal wave functions, Fourier analysis, and uncertainty – V: The discrete case...

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

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

in the spectroscopic analysis of the quadrupole moments while the prolate spheroid shape of the nucleon arises from analysis of the intrinsic quadruple...

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

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

original on 2011-07-18. Retrieved 2009-03-25. Fukushima, Toshio (2014). "Prolate spheroidal harmonic expansion of gravitational field". Astrophys. J. 147 (6):...

prolate spheroid touching the sphere at the poles, with an equatorial radius (extraordinary index) equal to the polar radius of the oblate spheroidal...

fixed centers. It is well known that the Schrödinger wave equation is separable in prolate spheroidal coordinates and can be decoupled into two ordinary...

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

be of varying geometric shape; spheres, discs, ellipsoids and prolate or oblate spheroids, and would be either isolated or set in a repeating pattern as...

and polar radii of Huygens's oblate spheroid while preserving the polar direction, we obtain a prolate spheroid touching the sphere at the equator. A plane...

correlation). The wave equation (a partial differential equation) separates into two coupled ordinary differential equations when using prolate spheroidal coordinates...

along its major axis to produce an ellipsoidal mirror (specifically, a prolate spheroid), this property holds for all rays out of the source. Alternatively...

Mathieu equation (best example), Lamé and ellipsoidal wave equations, oblate and prolate spheroidal wave equations, and equations with anharmonic potentials...

Johannes; Osten, Wolfgang (20 July 2017). "Measuring aspheres quickly: tilted wave interferometry". Optical Engineering. 56 (11): 111713. doi:10.1117/1.OE.56...

sufficiently deep ocean under the tidal force of a single deforming body is a prolate spheroid (essentially a three-dimensional oval) with major axis directed toward...

behavior of particles such as red blood cells (as oblate spheroids) or long thin tubes (as prolate ellipsoids) allowing the approximation of the dielectrophoretic...

"What Do a Submarine, a Rocket and a Football Have in Common? Why the prolate spheroid is the shape for success" (Scientific American, November 8, 2010) Conservation...

forces from the planet it orbits rather than flattened, resulting in a prolate spheroid shape where the equator is covered by an atmosphere but the poles rise...

shock wave propagation within the explosive mass, this requires the pit to be a prolate spheroid, that is, roughly egg shaped. The shock wave first reaches...

drag of a simplified model of the body, that can be approached by a prolate spheroid, and the sustainable level of energy output by the muscles. A first...