日本东京理科大学文凭毕业证真实样板《做证微fuk7778》2MiBwz
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21: 10.36 Other Differential Equations
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►The quantity in (10.13.1)–(10.13.6) and (10.13.8) can be replaced by if at the same time the symbol in the given solutions is replaced by .
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10.36.1
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10.36.2
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22: 29.4 Graphics
23: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
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►For
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is the number of permutations of with cycles of length 1, cycles of length 2, , and cycles of length :
… is the number of set partitions of with subsets of size 1, subsets of size 2, , and subsets of size :
…For each all possible values of are covered.
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►where the summation is over all nonnegative integers such that .
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24: 10.13 Other Differential Equations
25: 18.8 Differential Equations
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26: 22.7 Landen Transformations
27: 29.21 Tables
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Ince (1940a) tabulates the eigenvalues , (with and interchanged) for , , and . Precision is 4D.
Arscott and Khabaza (1962) tabulates the coefficients of the polynomials in Table 29.12.1 (normalized so that the numerically largest coefficient is unity, i.e. monic polynomials), and the corresponding eigenvalues for , . Equations from §29.6 can be used to transform to the normalization adopted in this chapter. Precision is 6S.
28: 29.3 Definitions and Basic Properties
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►They are denoted by , , , , where ; see Table 29.3.1.
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►The quantity satisfies equation (29.3.10) with
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►The quantity satisfies equation (29.3.10) with
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►The quantity satisfies equation (29.3.10) with
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►The eigenfunctions corresponding to the eigenvalues of §29.3(i) are denoted by , , , .
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29: 10.49 Explicit Formulas
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►Again, with as in (10.49.1),
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is sometimes called the Bessel polynomial of degree
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