representations%20by%20Euler%E2%80%93Maclaurin%20formula
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21—30 of 596 matching pages
21: Gergő Nemes
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►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions.
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22: 36 Integrals with Coalescing Saddles
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23: 27.2 Functions
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►Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes.
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►This is the number of positive integers that are relatively prime to ; is Euler’s totient.
►If , then the Euler–Fermat theorem states that
…The numbers are relatively prime to and distinct (mod ).
…Note that .
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24: 26.13 Permutations: Cycle Notation
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►An explicit representation of can be given by the matrix:
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25: 33.24 Tables
26: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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Euler sums and contour integral representations.
Experiment. Math. 7 (1), pp. 15–35.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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27: 18.5 Explicit Representations
§18.5 Explicit Representations
… ►Chebyshev
… ►§18.5(ii) Rodrigues Formulas
… ►Related formula: … ►28: Bibliography P
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An asymptotic representation for
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Methods Appl. Anal. 4 (4), pp. 449–470.
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A new basis for the representation of the rotation group. Lamé and Heun polynomials.
J. Mathematical Phys. 14 (8), pp. 1130–1139.
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Tables of the Incomplete -function.
Biometrika Office, Cambridge University Press, Cambridge.
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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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Stacking models of vesicles and compact clusters.
J. Statist. Phys. 80 (3–4), pp. 755–779.
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29: Bibliography C
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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On the representation of a large even integer as the sum of a prime and the product of at most two primes.
Kexue Tongbao (Foreign Lang. Ed.) 17, pp. 385–386.
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On a Tricomi series representation for the generalized exponential integral.
Internat. J. Comput. Math. 31, pp. 257–262.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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30: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems.
Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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On the representation of numbers as a sum of squares.
Quarterly Journal of Math. 48, pp. 93–104.
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