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1: 34.6 Definition: Symbol
§34.6 Definition: Symbol
►The symbol may be defined either in terms of symbols or equivalently in terms of symbols: ►
34.6.1
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34.6.2
►The symbol may also be written as a finite triple sum equivalent to a terminating generalized hypergeometric series of three variables with unit arguments.
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2: 19.2 Definitions
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►The principal values of and are even functions.
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§19.2(iv) A Related Function:
… ►Formulas involving that are customarily different for circular cases, ordinary hyperbolic cases, and (hyperbolic) Cauchy principal values, are united in a single formula by using . … ►When and are positive, is an inverse circular function if and an inverse hyperbolic function (or logarithm) if : …For the special cases of and see (19.6.15). …3: Bibliography H
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Solving Ordinary Differential Equations. I. Nonstiff Problems.
2nd edition, Springer Series in Computational Mathematics, Vol. 8, Springer-Verlag, Berlin.
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Lamé polynomials of large order.
SIAM J. Math. Anal. 8 (5), pp. 800–842.
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Calculation of Coulomb wave functions for high energies.
Phys. Rev. 54 (8), pp. 627–628.
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On congruences involving Bernoulli numbers and irregular primes. II.
Rep. Fac. Sci. Technol. Meijo Univ. 31, pp. 1–8.
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Coulomb Wave Functions.
In Handbuch der Physik, Bd. 41/1, S. Flügge (Ed.),
pp. 408–465.
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4: 3.4 Differentiation
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►The are the differentiated Lagrangian interpolation coefficients:
…where is as in (3.3.10).
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►where is a simple closed contour described in the positive rotational sense such that and its interior lie in the domain of analyticity of , and is interior to .
Taking to be a circle of radius centered at , we obtain
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5: 24.2 Definitions and Generating Functions
6: 27.2 Functions
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27.2.9
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►It is the special case of the function that counts the number of ways of expressing as the product of factors, with the order of factors taken into account.
…Note that .
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►Table 27.2.2 tabulates the Euler totient function , the divisor function (), and the sum of the divisors (), for .
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7: 26.6 Other Lattice Path Numbers
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Delannoy Number
► is the number of paths from to that are composed of directed line segments of the form , , or . … ► … ► … ► …8: 8 Incomplete Gamma and Related
Functions
Chapter 8 Incomplete Gamma and Related Functions
…9: 1.12 Continued Fractions
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is called the th approximant or convergent to
.
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►Define
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►A contraction of a continued fraction is a continued fraction whose convergents form a subsequence of the convergents of .
Conversely, is called an extension of .
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►Then the convergents satisfy
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10: Bibliography
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Tables of for Complex Argument.
Pergamon Press, New York.
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Supplement to a paper “On the intensity of light in the neighbourhood of a caustic”.
Trans. Camb. Phil. Soc. 8, pp. 595–599.
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Frequency response characteristics of the multiport planar elliptic patch.
IEEE Trans. Microwave Theory Tech. 40 (8), pp. 1726–1730.
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Algorithm 588. Fast Hankel transforms using related and lagged convolutions.
ACM Trans. Math. Software 8 (4), pp. 369–370.
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Chiral-symmetry breaking in QCD. I. The infrared domain.
Phys. Rev. D (3) 37 (8), pp. 2290–2295.
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