巴斯克大学商业管理文凭证书【假证加微aptao168】2tilULm
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11: 28.14 Fourier Series
12: 30.16 Methods of Computation
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►and real eigenvalues , , , , arranged in ascending order of magnitude.
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►For , , ,
…which yields .
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►If is known, then can be found by summing (30.8.1).
The coefficients are computed as the recessive solution of (30.8.4) (§3.6), and normalized via (30.8.5).
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13: 28.4 Fourier Series
14: 19.3 Graphics
15: 10.53 Power Series
16: 28.16 Asymptotic Expansions for Large
17: 28.6 Expansions for Small
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►For more details on these expansions and recurrence relations for the coefficients see Frenkel and Portugal (2001, §2).
►The coefficients of the power series of , and also , are the same until the terms in and , respectively.
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►Here for , for , and for and .
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►where is the unique root of the equation in the interval , and .
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►For more details on these expansions and recurrence relations for the coefficients see Frenkel and Portugal (2001, §2).
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18: 28.15 Expansions for Small
19: 29.7 Asymptotic Expansions
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29.7.4
►The same Poincaré expansion holds for , since
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29.7.6
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►In Müller (1966c) it is shown how these expansions lead to asymptotic expansions for the Lamé functions and .
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