New Online Book! Handbook of Mathematical Functions (AMS55) Conversion & Calculation Home >> Reference Information Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (AMS55) Purchase the electronic edition of this book in Adobe PDF format! FIRST | PREVIOUS | NEXT | LAST | CONTENTS | PAGE | ABOUT | SMALL | MEDIUM | LARGE Below is the OCR-scanned text from this page: 24. Combinatorial Analysis K. GOLDBERG,’ M. NEWMAN: E. HAYNSWORTH~ Con tents Mathematical Properties . . . . . . . . . . . . . 24.1. Basic Numbers . . . . . . . . . . . . . 24.1.1 Binomial Coefficients . . . . . . . 24.1.2 Multinomial Coefficients . . . . . . 24.1.3 Stirling Numbers of the First Kind . 24.1.4 Stirling Numbers of the Second Kind 24.2. Partitions . . . . . . . . . . . . . . . 24.2.1 Unrestricted Partitions . . . . . . . 24.2.2 Partitions Into Distinct Parts . . . . 24.3. Number Theoretic Functions . . . . . . . 24.3.1 The Mobius Function . . . . . . . 24.3.2 The Euler Function . . . . . . . . 24.3.3 Divisor Functions . . . . . . . . . 24.3.4 Primitive Roots . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 24.1. Binomial Coefficients . . . . . . . . . . . . . . n 1 5 0 , m125 Table 24.2. Multinomials (Including a List of Partitions) . . . . . . n<10 Table 24.3. Stirling Numbers of the First Kind SLm). . . . . . . . . n 1 2 5 Table 24.4. Stirling Numbers of the Second Kind %;Lm) . . . . . . . n 5 2 5 Table 24.5. Number of Partitions and Partitions Into Distinct Parts . P h ) , a h > , n 1 5 0 0 a b ) , d n ) , a ~ ( n > , n i l 0 0 0 Table 24.6. Arithmetic Functions . . . . . . . . . . . . . . . . Table 24.7. Factorizations . . . . . . . . . . . . . . . . . . . . n<10000 Table 24.8. Primitive Roots, Factorization of p- 1 . . . . . . . . . n<10000 Table 24.9. Primes . . . . . . . . . . . . . . . . . . . . . . . p s i 0 5 Page 822 822 822 823 824 824 825 82 5 825 826 826 826 827 827 827 828 83 1 833 835 836 840 844 864 670 1. * National Bureau of Standards. 3 National Bureau of Standards. (Presently, Auburn University.) 82 1 ~~~~ ~- _______ ______~ ~______ ______~ ~~ ~~~~ The page scan image above, and the text in the text box above, are contributions of the National Institute of Standards and Technology that are not subject to copyright in the United States. ©2000 ConvertIt.com, Inc. All rights reserved. Terms of Use.