组合数学3-6差分表与Stìrlìng数.ppt

3.6 差分序列和Stirling数 3.6.1 差分 3.6.1.1 差分算子 3.6.1.2 差分表 3.6.1.3 移位算子 3.6.1.4 算子运算 3.6.1.5 牛顿公式 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 3.6 差分序列和Stirling数 3.6.2 Stirling数 3.6.2.1 第二类Stirling数的定义 3.6.2.2 第二类Stirling数递归 3.6.2.3 第二类Stirling数 3.6.2.4 第一类Stirling数 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 3.6.1.1 差分算子 差分算子△ 设序列hn(n＝0,1,2,…)，递归定义 0阶差分序列△0hn＝hn(n＝0,1,2,…) 1阶差分序列△1hn＝hn+1－hn(n＝0,1,2,…) k阶差分序列 △khn＝△(△k-1hn) ＝△k-1hn+1－△k-1hn (n＝0,1,2,…) Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 3.6.1.2 差分表 数列的差分表 设序列hn(n＝0,1,2,…) h0 h1 h2 h3 h4 … △1h0 △1h1 △1h2 △1h3 △2h0 △2h1 △2h2 △3h0 △3h1 0条对角线 … Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 3.6.1.2 差分表 序列hn＝n3＋n(n＝0,1,2,…)的差分表 0 2 10 30 68 130 … 2 8 20 38 62 6 12 18 24 6 6 6 0 0 … Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 3.6.1.2 差分表 定理3.6.1令序列hn(n＝0,1,2,…)的一般项是n的t次多项式，即 hn＝atnt＋at-1nt-1＋…＋a1n＋a0 则对任意n(n＝0,1,2,…),△t+1hn＝0 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 3.6.1.3 移位算子 移位算子E 设序列hn(n＝0,1,2,…)，定义 Ekhn＝hn+k(n＝0,1,2,…) 恒等算子I 设序列hn(n＝0,1,2,…)，定义 Ikhn＝hn(n＝0,1,2,…) Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 3.6.1.4 算子运算 算子运算 设