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1: 20 Theta Functions
Chapter 20 Theta Functions
…2: 26.13 Permutations: Cycle Notation
3: 26.8 Set Partitions: Stirling Numbers
§26.8(i) Definitions
… ► … ►§26.8(ii) Generating Functions
… ►§26.8(iv) Recurrence Relations
… ►§26.8(v) Identities
…4: 26.21 Tables
§26.21 Tables
►Abramowitz and Stegun (1964, Chapter 24) tabulates binomial coefficients for up to 50 and up to 25; extends Table 26.4.1 to ; tabulates Stirling numbers of the first and second kinds, and , for up to 25 and up to ; tabulates partitions and partitions into distinct parts for up to 500. … ►It also contains a table of Gaussian polynomials up to . …5: 26.14 Permutations: Order Notation
6: 28 Mathieu Functions and Hill’s Equation
Chapter 28 Mathieu Functions and Hill’s Equation
…7: 26.1 Special Notation
real variable. |
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binomial coefficient. |
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Stirling numbers of the first kind. |
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Stirling numbers of the second kind. |
8: 10.75 Tables
British Association for the Advancement of Science (1937) tabulates , , , 7–8D; , , , 7–10D; , , , , , 8D. Also included are auxiliary functions to facilitate interpolation of the tables of , for small values of .
Bickley et al. (1952) tabulates or , or , , (.01 or .1) 10(.1) 20, 8S; , , , or , 10S.
The main tables in Abramowitz and Stegun (1964, Chapter 9) give , , , , 8D–10D or 10S; , , , ; , , , 8D; , , , , 5S; , , , , 9–10S.
Zhang and Jin (1996, pp. 240–250) tabulates , , , , , , 9S; , , , , , 10, 30, 50, 100, , , , , , , 5, 10, 50, 8S; real and imaginary parts of , , , , , 20(10)50, 100, , , 8S.
Kerimov and Skorokhodov (1984b) tabulates all zeros of the principal values of and , for , 9S.