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International Journal of Mathematical Education in Science and Technology, 1996We extend some earlier results while illustrating solution techniques commonly encountered by students in undergraduate and beginning graduate courses of mathematical analysis, differential equations, and engineering mathematics. Previously, Turan's inequality was established by using a technique known as the Prufer substitution.
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Atomic Eigenfunctions and Energies
Physical Review, 1932In \textsection{}1, the calculation of the nondiagonal elements of electrostatic interaction is sketched. In \textsection{}2, attention is called to the fact that the matrix elements of ${L}_{x}$ (the $x$-component of orbital angular momentum), as calculated between spherical harmonic eigenfunctions taken with positive phase, are negative when ${m}_{l}$
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On the Smallness of Isolated Eigenfunctions
American Journal of Mathematics, 1949which is satisfied by x yj(t) at t = 0). According to Weyl [3], p. 238, the assumption (2) precludes the existence of a A0 corresponding to which (3) had two linearly independent solutions of class (L2). Correspondingly, every boundary condition (5) determines for (1) a spectrum S(p), containing a (possibly vacuous) point spectrum P(p).
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