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1: 19.2 Definitions
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►where is a polynomial in while and are rational functions of .
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►Here are real parameters, and and are real or complex variables, with , .
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►If , then is pure imaginary.
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§19.2(iv) A Related Function:
… ►For the special cases of and see (19.6.15). …2: 34.6 Definition: Symbol
3: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
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is the number of ways of placing distinct objects into labeled boxes so that there are objects in the th box.
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►These are given by the following equations in which are nonnegative integers such that
… is the multinominal coefficient (26.4.2):
…For each all possible values of are covered.
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►where the summation is over all nonnegative integers such that .
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4: 34.7 Basic Properties: Symbol
5: 32.3 Graphics
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►Plots of solutions of with and for various values of , and the parabola .
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►Here is the solution of with and such that
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►Here is the solution of
…The corresponding solution of is given by
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6: 18.41 Tables
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►For () see §14.33.
►Abramowitz and Stegun (1964, Tables 22.4, 22.6, 22.11, and 22.13) tabulates , , , and for .
The ranges of are for and , and for and .
The precision is 10D, except for which is 6-11S.
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►For , , and see §3.5(v).
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7: 27.2 Functions
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►where are the distinct prime factors of , each exponent is positive, and is the number of distinct primes dividing .
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►Note that .
…Note that .
►In the following examples, are the exponents in the factorization of in (27.2.1).
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►Table 27.2.1 lists the first 100 prime numbers .
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8: 23.9 Laurent and Other Power Series
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►Let be the nearest lattice point to the origin, and define
…Explicit coefficients in terms of and are given up to in Abramowitz and Stegun (1964, p. 636).
►For , and with as in §23.3(i),
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►where , if either or , and
…For with and , see Abramowitz and Stegun (1964, p. 637).
9: 3.4 Differentiation
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►The are the differentiated Lagrangian interpolation coefficients:
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►where and .
►For the values of and used in the formulas below
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►For partial derivatives we use the notation .
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