numerically satisfactory solutions
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1: 14.21 Definitions and Basic Properties
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§14.21(ii) Numerically Satisfactory Solutions
►When and , a numerically satisfactory pair of solutions of (14.21.1) in the half-plane is given by and . …2: 11.2 Definitions
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§11.2(iii) Numerically Satisfactory Solutions
… ►When , , and , numerically satisfactory general solutions of (11.2.7) are given by … ►When and , numerically satisfactory general solutions of (11.2.7) are given by … ►When , numerically satisfactory general solutions of (11.2.9) are given by …(11.2.17) applies when with bounded away from the origin.3: 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). … ►4: 2.7 Differential Equations
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§2.7(iv) Numerically Satisfactory Solutions
… ►This kind of cancellation cannot take place with and , and for this reason, and following Miller (1950), we call and a numerically satisfactory pair of solutions. … ►In consequence, if a differential equation has more than one singularity in the extended plane, then usually more than two standard solutions need to be chosen in order to have numerically satisfactory representations everywhere. ►In oscillatory intervals, and again following Miller (1950), we call a pair of solutions numerically satisfactory if asymptotically they have the same amplitude and are out of phase.5: 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). ► …6: 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 . … ►7: 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 . …8: 13.2 Definitions and Basic Properties
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§13.2(v) Numerically Satisfactory Solutions
►Fundamental pairs of solutions of (13.2.1) that are numerically satisfactory (§2.7(iv)) in the neighborhood of infinity are … ►A fundamental pair of solutions that is numerically satisfactory near the origin is … ► …9: 10.47 Definitions and Basic Properties
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