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31—40 of 237 matching pages
31: 24.1 Special Notation
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integers, nonnegative unless stated otherwise. | |
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greatest common divisor of . | |
and relatively prime. |
32: 28.17 Stability as
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►If all solutions of (28.2.1) are bounded when along the real axis, then the corresponding pair of parameters is called stable.
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►However, if , then always comprises an unstable pair.
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33: 18.31 Bernstein–Szegő Polynomials
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►The Bernstein–Szegő polynomials
, , are orthogonal on with respect to three types of weight function: , , .
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34: 18.39 Applications in the Physical Sciences
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►in which case the probability density is time-independent, as .
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►where the orthogonality measure is now ,
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►Orthogonality, with measure for , for fixed
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►normalized with measure , .
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►which maps onto .
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35: 7.24 Approximations
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Schonfelder (1978) gives coefficients of Chebyshev expansions for on , for on , and for on (30D).
Shepherd and Laframboise (1981) gives coefficients of Chebyshev series for on (22D).
36: 23.15 Definitions
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►The set of all bilinear transformations of this form is denoted by SL (Serre (1973, p. 77)).
►A modular function
is a function of that is meromorphic in the half-plane , and has the property that for all , or for all belonging to a subgroup of SL,
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37: 1.6 Vectors and Vector-Valued Functions
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►Note: The terminology open and closed sets and boundary
points in the plane that is used in this subsection and §1.6(v) is analogous to that introduced for the complex plane in §1.9(ii).
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►A path , , is a reparametrization of , , if and with differentiable and monotonic.
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►and be the closed and bounded point set in the plane having a simple closed curve as boundary.
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►with , an open set in the plane.
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►For a surface of revolution, , , about the -axis,
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38: 26.9 Integer Partitions: Restricted Number and Part Size
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►It is also equal to the number of lattice paths from to that have exactly vertices , , , above and to the left of the lattice path.
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39: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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►Let or or or be a (possibly infinite, or semi-infinite) interval in .
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Hermite’s Differential Equation,
►The space is now the full real line, . … ►Example 1: Bessel–Hankel Transform,
… ►Pick . …40: 5.3 Graphics
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