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Reference.org
Prolate spheroidal wave function
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, prolate spheroidal wave functions are <a href="/facts/Eigenfunctions/62EJS0XB">eigenfunctions</a> of the Laplacian in <a href="/facts/Prolate_spheroidal_coordinates/YqNbjpHh">prolate spheroidal coordinates</a>, adapted to boundary conditions on certain ellipsoids of revolution (an ellipse rotated around its long axis, “cigar shape“). Related are the <a href="/facts/Oblate_spheroidal_wave_functions/DAD4jjzL">oblate spheroidal wave functions</a> (“pancake shaped” ellipsoid). </p>