negative%20definite
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31—40 of 211 matching pages
31: 9.9 Zeros
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►On the real line, , , , each have an infinite number of zeros, all of which are negative.
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9.9.6
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9.9.7
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9.9.8
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9.9.9
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32: 8 Incomplete Gamma and Related
Functions
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33: 28 Mathieu Functions and Hill’s Equation
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34: 4.3 Graphics
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►Figure 4.3.2 illustrates the conformal mapping of the strip onto the whole -plane cut along the negative real axis, where and (principal value).
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35: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
36: 23 Weierstrass Elliptic and Modular
Functions
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37: 18.39 Applications in the Physical Sciences
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►The non-relativistic Schrödinger equation describing a single, bound (negative energy) electron, in an eigenstate of energy is:
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►where is a real, positive, scaling factor, and a non-negative integer.
►As in this subsection both positive (repulsive) and negative (attractive) Coulomb interactions are discussed, the prefactor of in (18.39.43) has been set to , rather than the of (18.39.28) implying that is an attractive interaction, being repulsive.
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►The polynomials , for both positive and negative
, define the Coulomb–Pollaczek polynomials (CP OP’s in what follows), see Yamani and Reinhardt (1975, Appendix B, and §IV).
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►Note that violation of the Favard inequality, possible when , results in a zero or negative weight function.
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38: 35.8 Generalized Hypergeometric Functions of Matrix Argument
39: Bibliography L
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Algorithm 917: complex double-precision evaluation of the Wright function.
ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Functions on a parabolic cylinder with a negative integer index.
Differ. Uravn. 21 (11), pp. 2001–2003, 2024 (Russian).
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40: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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A program for computing the Riemann zeta function for complex argument.
Comput. Phys. Comm. 20 (3), pp. 441–445.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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Bessel functions and modular relations of higher type and hyperbolic differential equations.
Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.
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