愛知東邦大学学士成绩单【购证 微kaa77788】54Z
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1: 10.29 Recurrence Relations and Derivatives
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►With defined as in §10.25(ii),
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►For results on modified quotients of the form see Onoe (1955) and Onoe (1956).
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2: 33.22 Particle Scattering and Atomic and Molecular Spectra
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►With denoting here the elementary charge, the Coulomb potential between two point particles with charges and masses separated by a distance is , where are atomic numbers, is the electric constant, is the fine structure constant, and is the reduced Planck’s constant.
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►In these applications, the -scaled variables and are more convenient.
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Scaling
►The -scaled variables and of §33.14 are given by … ►Resolution of the ambiguous signs in (33.22.11), (33.22.12) depends on the sign of in (33.22.3). …3: 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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4: 25.3 Graphics
5: 35.2 Laplace Transform
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►For any complex symmetric matrix ,
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35.2.1
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►Then (35.2.1) converges absolutely on the region , and is a complex analytic function of all elements of .
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35.2.2
►where the integral is taken over all such that and ranges over .
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6: 25.10 Zeros
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►Calculations relating to the zeros on the critical line make use of the real-valued function
…is chosen to make real, and assumes its principal value.
Because , vanishes at the zeros of , which can be separated by observing sign changes of .
Because changes sign infinitely often, has infinitely many zeros with real.
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►Sign changes of are determined by multiplying (25.9.3) by to obtain the Riemann–Siegel formula:
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7: 35.4 Partitions and Zonal Polynomials
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►For any partition , the zonal polynomial
is defined by the properties
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35.4.4
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35.4.5
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►Therefore is a symmetric polynomial in the eigenvalues of .
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35.4.7
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8: 10.44 Sums
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10.44.1
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►If and the upper signs are taken, then the restriction on is unnecessary.
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10.44.3
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►The restriction is unnecessary when and is an integer.
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9: 19.19 Taylor and Related Series
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►The number of terms in can be greatly reduced by using variables with chosen to make .
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19.19.7
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10: 18.39 Applications in the Physical Sciences
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►thus recapitulating, for , line 11 of Table 18.8.1, now shown with explicit normalization for the measure .
This is also the normalization and notation of Chapter 33 for , and the notation of Weinberg (2013, Chapter 2).
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►As in this subsection both positive (repulsive) and negative (attractive) Coulomb interactions are discussed, the prefactor of in (18.39.43) has been set to , rather than the of (18.39.28) implying that is an attractive interaction, being repulsive.
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►The polynomials , for both positive and negative , define the Coulomb–Pollaczek polynomials (CP OP’s in what follows), see Yamani and Reinhardt (1975, Appendix B, and §IV).
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►Note that violation of the Favard inequality, possible when , results in a zero or negative weight function.
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