normalizing factor
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1: 3.6 Linear Difference Equations
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►It therefore remains to apply a normalizing factor
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►The normalizing factor
can be the true value of divided by its trial value, or can be chosen to satisfy a known property of the wanted solution of the form
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2: 3.7 Ordinary Differential Equations
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►The eigenvalues are simple, that is, there is only one corresponding eigenfunction (apart from a normalization factor), and when ordered increasingly the eigenvalues satisfy
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3: 18.39 Applications in the Physical Sciences
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►All are written in the same form as the product of three factors: the square root of a weight function , the corresponding OP or EOP, and constant factors ensuring unit normalization.
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►With the normalization factor
the are orthonormal in .
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4: 28.5 Second Solutions ,
5: 33.13 Complex Variable and Parameters
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33.13.2
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6: Bibliography C
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Reduction theorems for elliptic integrands with the square root of two quadratic factors.
J. Comput. Appl. Math. 118 (1-2), pp. 71–85.
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Normal elliptic integrals of the first and second kinds.
Duke Math. J. 31 (3), pp. 405–419.
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Demagnetization factors for general ellipsoids.
J. Appl. Phys. 70 (6), pp. 2911–2914.
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Algorithm AS 24: From normal integral to deviate.
Appl. Statist. 18 (3), pp. 290–293.
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7: 19.16 Definitions
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19.16.1
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19.16.2
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19.16.2_5
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19.16.4
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►It should be noted that the integrals (19.16.1)–(19.16.2_5) have been normalized so that .
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8: 18.2 General Orthogonal Polynomials
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►The orthogonality relations (18.2.1)–(18.2.3) each determine the polynomials uniquely up to constant factors, which may be fixed by suitable standardizations.
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►If the polynomials () are orthogonal on a finite set of distinct points as in (18.2.3), then the polynomial of degree , up to a constant factor defined by (18.2.8) or (18.2.10), vanishes on .
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►, of the form ) nor is it necessarily unique, up to a positive constant factor.
However, if OP’s have an orthogonality relation on a bounded interval, then their orthogonality measure is unique, up to a positive constant factor.
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9: 28.12 Definitions and Basic Properties
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►In consequence, for the Floquet solutions the factor
in (28.2.14) is no longer .
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28.12.2
►As in §28.7 values of for which (28.2.16) has simple roots are called normal values with respect to .
For real values of and all the are real, and is normal.
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►If is a normal value of the corresponding equation (28.2.16), then these functions are uniquely determined as analytic functions of and by the normalization
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10: 10.22 Integrals
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10.22.72
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