About the Project

愛知東邦大学学士成绩单【购证 微kaa77788】54Z

AdvancedHelp

The term"kaa77788" was not found.Possible alternative term: "27789".

(0.003 seconds)

1—10 of 60 matching pages

1: 10.29 Recurrence Relations and Derivatives
With 𝒵 ν ( z ) defined as in §10.25(ii),
𝒵 ν 1 ( z ) 𝒵 ν + 1 ( z ) = ( 2 ν / z ) 𝒵 ν ( z ) ,
𝒵 ν 1 ( z ) + 𝒵 ν + 1 ( z ) = 2 𝒵 ν ( z ) .
𝒵 ν ( z ) = 𝒵 ν 1 ( z ) ( ν / z ) 𝒵 ν ( z ) ,
For results on modified quotients of the form z 𝒵 ν ± 1 ( z ) / 𝒵 ν ( z ) see Onoe (1955) and Onoe (1956). …
2: 33.22 Particle Scattering and Atomic and Molecular Spectra
With e denoting here the elementary charge, the Coulomb potential between two point particles with charges Z 1 e , Z 2 e and masses m 1 , m 2 separated by a distance s is V ( s ) = Z 1 Z 2 e 2 / ( 4 π ε 0 s ) = Z 1 Z 2 α c / s , where Z j are atomic numbers, ε 0 is the electric constant, α is the fine structure constant, and is the reduced Planck’s constant. … In these applications, the Z -scaled variables r and ϵ are more convenient.
Z Scaling
The Z -scaled variables r and ϵ of §33.14 are given by … Resolution of the ambiguous signs in (33.22.11), (33.22.12) depends on the sign of Z / 𝗄 in (33.22.3). …
3: 10.36 Other Differential Equations
The quantity λ 2 in (10.13.1)–(10.13.6) and (10.13.8) can be replaced by λ 2 if at the same time the symbol 𝒞 in the given solutions is replaced by 𝒵 . …
10.36.1 z 2 ( z 2 + ν 2 ) w ′′ + z ( z 2 + 3 ν 2 ) w ( ( z 2 + ν 2 ) 2 + z 2 ν 2 ) w = 0 , w = 𝒵 ν ( z ) ,
10.36.2 z 2 w ′′ + z ( 1 ± 2 z ) w + ( ± z ν 2 ) w = 0 , w = e z 𝒵 ν ( z ) .
4: 25.3 Graphics
See accompanying text
Figure 25.3.4: Z ( t ) , 0 t 50 . Z ( t ) and ζ ( 1 2 + i t ) have the same zeros. … Magnify
See accompanying text
Figure 25.3.5: Z ( t ) , 1000 t 1050 . Magnify
See accompanying text
Figure 25.3.6: Z ( t ) , 10000 t 10050 . Magnify
5: 35.2 Laplace Transform
For any complex symmetric matrix 𝐙 ,
35.2.1 g ( 𝐙 ) = 𝛀 etr ( 𝐙 𝐗 ) f ( 𝐗 ) d 𝐗 ,
Then (35.2.1) converges absolutely on the region ( 𝐙 ) > 𝐗 0 , and g ( 𝐙 ) is a complex analytic function of all elements z j , k of 𝐙 . … where the integral is taken over all 𝐙 = 𝐔 + i 𝐕 such that 𝐔 > 𝐗 0 and 𝐕 ranges over 𝓢 . …
6: 25.10 Zeros
Calculations relating to the zeros on the critical line make use of the real-valued function …is chosen to make Z ( t ) real, and ph Γ ( 1 4 + 1 2 i t ) assumes its principal value. Because | Z ( t ) | = | ζ ( 1 2 + i t ) | , Z ( t ) vanishes at the zeros of ζ ( 1 2 + i t ) , which can be separated by observing sign changes of Z ( t ) . Because Z ( t ) changes sign infinitely often, ζ ( 1 2 + i t ) has infinitely many zeros with t real. … Sign changes of Z ( t ) are determined by multiplying (25.9.3) by exp ( i ϑ ( t ) ) to obtain the Riemann–Siegel formula: …
7: 35.4 Partitions and Zonal Polynomials
For any partition κ , the zonal polynomial Z κ : 𝓢 is defined by the properties …
35.4.4 Z κ ( 𝟎 ) = { 1 , κ = ( 0 , , 0 ) , 0 , κ ( 0 , , 0 ) .
Therefore Z κ ( 𝐓 ) is a symmetric polynomial in the eigenvalues of 𝐓 . …
8: 10.44 Sums
10.44.1 𝒵 ν ( λ z ) = λ ± ν k = 0 ( λ 2 1 ) k ( 1 2 z ) k k ! 𝒵 ν ± k ( z ) , | λ 2 1 | < 1 .
If 𝒵 = I and the upper signs are taken, then the restriction on λ is unnecessary. …
10.44.3 𝒵 ν ( u ± v ) = k = ( ± 1 ) k 𝒵 ν + k ( u ) I k ( v ) , | v | < | u | .
The restriction | v | < | u | is unnecessary when 𝒵 = I and ν is an integer. …
9: 19.19 Taylor and Related Series
The number of terms in T N can be greatly reduced by using variables 𝐙 = 𝟏 ( 𝐳 / A ) with A chosen to make E 1 ( 𝐙 ) = 0 . …
Z j = 1 ( z j / A ) ,
E 1 ( 𝐙 ) = 0 , | Z j | < 1 .
10: 18.39 Applications in the Physical Sciences
thus recapitulating, for Z = 1 , line 11 of Table 18.8.1, now shown with explicit normalization for the measure d r . This is also the normalization and notation of Chapter 33 for Z = 1 , and the notation of Weinberg (2013, Chapter 2). … As in this subsection both positive (repulsive) and negative (attractive) Coulomb interactions are discussed, the prefactor of Z / r in (18.39.43) has been set to + 1 , rather than the 1 of (18.39.28) implying that Z < 0 is an attractive interaction, Z > 0 being repulsive. … The polynomials P N ( l + 1 ) ( x ; 2 Z s , 2 Z s ) , for both positive and negative Z , define the Coulomb–Pollaczek polynomials (CP OP’s in what follows), see Yamani and Reinhardt (1975, Appendix B, and §IV). … Note that violation of the Favard inequality, l + 1 + ( 2 Z / s ) > 0 , possible when Z < 0 , results in a zero or negative weight function. …