numerically satisfactory pairs
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1: 10.25 Definitions
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§10.25(iii) Numerically Satisfactory Pairs of Solutions
►Table 10.25.1 lists numerically satisfactory pairs of solutions (§2.7(iv)) of (10.25.1). … ►2: 9.2 Differential Equation
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§9.2(iii) Numerically Satisfactory Pairs of Solutions
►Table 9.2.1 lists numerically satisfactory pairs of solutions of (9.2.1) for the stated intervals or regions; compare §2.7(iv). ► …3: 10.2 Definitions
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§10.2(iii) Numerically Satisfactory Pairs of Solutions
►Table 10.2.1 lists numerically satisfactory pairs of solutions (§2.7(iv)) of (10.2.1) for the stated intervals or regions in the case . … ►4: 10.45 Functions of Imaginary Order
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►In consequence of (10.45.5)–(10.45.7), and comprise a numerically satisfactory pair of solutions of (10.45.1) when is large, and either and , or and , comprise a numerically satisfactory pair when is small, depending whether or .
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5: 10.24 Functions of Imaginary Order
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►In consequence of (10.24.6), when is large and comprise a numerically satisfactory pair of solutions of (10.24.1); compare §2.7(iv).
Also, in consequence of (10.24.7)–(10.24.9), when is small either and or and comprise a numerically satisfactory pair depending whether or .
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6: 10.47 Definitions and Basic Properties
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§10.47(iii) Numerically Satisfactory Pairs of Solutions
►For (10.47.1) numerically satisfactory pairs of solutions are given by Table 10.2.1 with the symbols , , , and replaced by , , , and , respectively. ►For (10.47.2) numerically satisfactory pairs of solutions are and in the right half of the -plane, and and in the left half of the -plane. …7: 12.2 Differential Equations
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►For real values of
, numerically satisfactory pairs of solutions (§2.7(iv)) of (12.2.2) are and when is positive, or and when is negative.
For (12.2.3) and comprise a numerically satisfactory pair, for all .
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►In , for , and comprise a numerically satisfactory pair of solutions in the half-plane .
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8: 14.2 Differential Equations
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§14.2(iii) Numerically Satisfactory Solutions
… ►Hence they comprise a numerically satisfactory pair of solutions (§2.7(iv)) of (14.2.2) in the interval . When , or , and are linearly dependent, and in these cases either may be paired with almost any linearly independent solution to form a numerically satisfactory pair. … ►Hence they comprise a numerically satisfactory pair of solutions of (14.2.2) in the interval . With the same conditions, and comprise a numerically satisfactory pair of solutions in the interval . …9: 14.21 Definitions and Basic Properties
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►When and , a numerically satisfactory pair of solutions of (14.21.1) in the half-plane is given by and .
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10: 28.8 Asymptotic Expansions for Large
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►Barrett (1981) supplies asymptotic approximations for numerically satisfactory pairs of solutions of both Mathieu’s equation (28.2.1) and the modified Mathieu equation (28.20.1).
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►Dunster (1994a) supplies uniform asymptotic approximations for numerically satisfactory pairs of solutions of Mathieu’s equation (28.2.1).
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