inversion numbers
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31—40 of 49 matching pages
31: 36.7 Zeros
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►Near , and for small and , the modulus has the symmetry of a lattice with a rhombohedral unit cell that has a mirror plane and an inverse threefold axis whose and repeat distances are given by
…, ), the number of rings in the th row, measured from the origin and before the transition to hairpins, is given by
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32: 3.5 Quadrature
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►For the Bernoulli numbers
see §24.2(i).
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►The remainder is given by
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Example. Laplace Transform Inversion
… ►In fact from (7.14.4) and the inversion formula for the Laplace transform (§1.14(iii)) we have … ►A special case is the rule for Hilbert transforms (§1.14(v)): …33: 25.5 Integral Representations
34: 22.18 Mathematical Applications
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Lemniscate
… ►Inversely: … ►See Akhiezer (1990, Chapter 8) and McKean and Moll (1999, Chapter 2) for discussions of the inverse mapping. … ►The theory of elliptic functions brings together complex analysis, algebraic curves, number theory, and geometry: Lang (1987), Siegel (1988), and Serre (1973).35: 3.11 Approximation Techniques
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Laplace Transform Inversion
►Numerical inversion of the Laplace transform (§1.14(iii)) … ►Here , , is a given set of distinct real points and . … ►In consequence of this structure the number of operations can be reduced to operations. … ►For many applications a spline function is a more adaptable approximating tool than the Lagrange interpolation polynomial involving a comparable number of parameters; see §3.3(i), where a single polynomial is used for interpolating on the complete interval . …36: Guide to Searching the DLMF
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term:
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phrase:
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proximity operator:
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a textual word, a number, or a math symbol.
any double-quoted sequence of textual words and numbers.
adj, prec/n, and near/n, where n is any positive natural number.
$ |
stands for any number of alphanumeric characters |
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All the inverse trigonometric functions (arcsin vs. Arcsin, etc.).
37: 1.10 Functions of a Complex Variable
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►Let and be real or complex numbers that are not integers.
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§1.10(vii) Inverse Functions
►Lagrange Inversion Theorem
… ►Extended Inversion Theorem
… ►(The integer may be greater than one to allow for a finite number of zero factors.) …38: Bibliography R
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Topics in Analytic Number Theory.
Springer-Verlag, New York.
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Some properties of Bernoulli’s numbers (J. Indian Math. Soc. 3 (1911), 219–234.).
In Collected Papers,
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Fourier analysis and signal processing by use of the Möbius inversion formula.
IEEE Trans. Acoustics, Speech, Signal Processing 38, pp. 458–470.
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Universality properties of Gaussian quadrature, the derivative rule, and a novel approach to Stieltjes inversion.
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Elementary Number Theory and its Applications.
5th edition, Addison-Wesley, Reading, MA.
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39: Bibliography K
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Poly-Bernoulli numbers.
J. Théor. Nombres Bordeaux 9 (1), pp. 221–228.
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On formulas involving both the Bernoulli and Fibonacci numbers.
Scripta Math. 23, pp. 27–35.
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Remark on -adic -Bernoulli numbers.
Adv. Stud. Contemp. Math. (Pusan) 1, pp. 127–136.
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Quantum Inverse Scattering Method and Correlation Functions.
Cambridge University Press, Cambridge.
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A Handbook of Methods of Approximate Fourier Transformation and Inversion of the Laplace Transformation.
Mir, Moscow.
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40: Bibliography B
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Periodic Bernoulli numbers, summation formulas and applications.
In Theory and Application of Special Functions (Proc. Advanced
Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis.,
1975),
pp. 143–189.
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Rational Chebyshev approximations for the inverse of the error function.
Math. Comp. 30 (136), pp. 827–830.
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Efficiency and Security of Cryptosystems Based on Number Theory.
Ph.D. Thesis, Swiss Federal Institute of Technology (ETH), Zurich.
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Asymptotics of Stirling numbers of the second kind.
Proc. Amer. Math. Soc. 42 (2), pp. 575–580.
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A Course in Computational Number Theory.
Key College Publishing, Emeryville, CA.
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