Quaintance J. Combinatorial identities for Stirling numbers: the unpublished notes of H.W.Gould (New Jerse, 2016). - ОГЛАВЛЕНИЕ / CONTENTS
Навигация
Архив выставки новых поступлений | Отечественные поступления | Иностранные поступления | Сиглы
ОбложкаQuaintance J. Combinatorial identities for Stirling numbers: the unpublished notes of H.W.Gould / J.Quaintance, H.W.Gould. - New Jersey: World scientific, 2016. - xv, 260 p.: tab. - Bibliogr.: p.253-255. - Ind.: p.257-260. - ISBN 978-981-4725-26-2
Шифр: (И/ В17-Q16) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
Foreword ...................................................... vii
Preface ........................................................ ix
Acknowledgments ................................................ xi
1  Basic Properties of Series ................................... 1
   1.1  General Considerations of Σnk=α ƒ(k)...................... 4
   1.2  Pascal's Identity in Evaluation of Series ............... 8
2  The Binomial Theorem ........................................ 13
   2.1  Newton's Binomial Theorem and the Geometric Series ..... 16
3  Iterative Series ............................................ 21
   3.1  Two Summation Interchange Formulas ..................... 23
   3.2  Gould's Convolution Formula ............................ 28
4  Two of Professor Gould's Favorite Algebraic Techniques ...... 35
   4.1  Coefficient Comparison ................................. 35
   4.2  The Fundamental Theorem of Algebra ..................... 42
5  Vandermonde Convolution ..................................... 49
   5.1  Five Basic Applications of the Vandermonde
        Convolution ............................................ 50
   5.2  An In-Depth Investigation Involving Equation (5.4) ..... 55
6  The nth Difference Operator and Euler's Finite
   Difference Theorem .......................................... 63
   6.1  Euler's Finite Difference Theorem ...................... 68
   6.2  Applications of Equation (6.16) ........................ 69
7  Melzak's Formula ............................................ 79
   7.1  Basic Applications of Melzak's Formula ................. 83
   7.2  Two Advanced Applications of Melzak's Formula .......... 86
   7.3  Partial Fraction Generalizations of Equation (7.1) ..... 89
   7.4  Lagrange Interpolation Theorem ........................  93
8  Generalized Derivative Formulas ............................ 101
   8.1  Leibniz Rule .......................................... 101
   8.2  Generalized Chain Rule ................................ 102
   8.3  Five Applications of Hoppe's Formula .................. 105
9  Stirling Numbers of the Second Kind S(n, k) ................ 113
   9.1  Euler's Formula for S(n, k) ........................... 118
   9.2  Grunert's Operational Formula ......................... 126
   9.3  Expansions of (℮x-1)n ................................. 131
                        x
   9.4  Bell Numbers .......................................... 133
10 Eulerian Numbers ........................................... 139
   10.1 Functional Expansions Involving Eulerian Numbers ...... 142
   10.2 Combinatorial Interpretation of A(n, m) ............... 144
11 Worpitzky Numbers .......................................... 147
   11.1 Polynomial Expansions from Nielsen's Formula .......... 152
   11.2 Nielsen's Expansion with Taylor's Theorem ............. 156
   11.3 Nielsen Numbers ....................................... 161
12 Stirling Numbers of the First Kind s(n, k) ................. 165
   12.1 Properties of s(n, k) ................................. 168
   12.2 Orthogonality Relationships for Stirling Numbers ...... 170
   12.3 Functional Expansions Involving s(n, k) ............... 173
   12.4 Derivative Expansions Involving s(n, k) ............... 175
13 Explicit Formulas for s(n, n - k) .......................... 177
   13.1 Schlдfli's Formula s(n, n - k) ........................ 180
   13.2 Proof of Equation (13.2) .............................. 185
14 Number Theoretic Definitions of Stirling Numbers ........... 191
   14.1 Relationships Between S1(n, k) and S2(n, k) ........... 196
   14.2 Hдgen Recurrences for S1(n, k) and S2(n, k) ........... 199
15 Bernoulli Numbers .......................................... 203
   15.1 Sum of Powers of Numbers .............................. 205
   15.2 Other Representations of Sp(n) ........................ 212
   15.3 Euler Polynomials and Euler Numbers ................... 217
   15.4 Polynomial Expansions Involving Bn(x) ................. 223
Appendix A  Newton-Gregory Expansions ......................... 227
Appendix В  Generalized Bernoulli and Euler Polynomials ....... 231
   B.1  Basic Properties of Bk(α)(x) and Ek(α)(x) ............... 232
   B.2  Generalized Bernoulli and Euler Polynomial
        Derivative Expansions ................................. 239
   B.3  Additional Considerations Involving Newton Series ..... 247
Bibliography .................................................. 253
Index ......................................................... 257

Архив выставки новых поступлений | Отечественные поступления | Иностранные поступления | Сиглы
 

[О библиотеке | Академгородок | Новости | Выставки | Ресурсы | Библиография | Партнеры | ИнфоЛоция | Поиск | English]
  Пожелания и письма: www@prometeus.nsc.ru
© 1997-2018 Отделение ГПНТБ СО РАН (Новосибирск)
Статистика доступов: архив | текущая статистика
 

Документ изменен: Thu Apr 5 17:11:40 2018. Размер: 8,613 bytes.
Посещение N 200 c 05.12.2017