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**Table of Integrals, Series, and Products, Seventh Edition**

A section not easy to decipher before everything, yet as soon as I obtained used to it this can be the easiest math reference e-book i have ever had. i will by no means want one other one except I put on this one out (not most probably. .. critical binding) and if I do i will need to get a similar ebook back. interesting background published within the introductions to prior types.

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**Example text**

1) = 2n n = (−1)n 2n + 1 k (−1)k 3. 3) (2n − 1)! 15810 n 1. 2k 2n − k n−k − 2k+1 2n − k − 1 n−k−1 k = 4n − 2k 2n − k n−k − 2k+1 2n − k − 1 n−k−1 k 2 = 4n − 2k 2n − k n−k − 2k+1 2n − k − 1 n−k−1 k 3 = (6n + 13)4n − 18n 2k 2n − k n−k − 2k+1 2n − k − 1 n−k−1 k 4 = (32n2 + 104n) k=1 n 2. k=1 n 3. k=1 n 4. 15910 n 1. k=0 2n n−k − 2n n−k−1 k= 1 n 4 − 2 2n n 2n n 2n n 3 · 4n 2n n 2n n − (60n + 75)4n 6 Numerical Series and Inﬁnite Products n 2. k=0 n 3. 16010 2n 1. k=n+1 n (−1)r 2. 211 uk = u1 + u2 + u3 + .

157 n n k 1. k=0 2 2n 2n k (−1)k 2. k=0 2n+1 k=0 n 4. 1) = 2n n = (−1)n 2n + 1 k (−1)k 3. 3) (2n − 1)! 15810 n 1. 2k 2n − k n−k − 2k+1 2n − k − 1 n−k−1 k = 4n − 2k 2n − k n−k − 2k+1 2n − k − 1 n−k−1 k 2 = 4n − 2k 2n − k n−k − 2k+1 2n − k − 1 n−k−1 k 3 = (6n + 13)4n − 18n 2k 2n − k n−k − 2k+1 2n − k − 1 n−k−1 k 4 = (32n2 + 104n) k=1 n 2. k=1 n 3. k=1 n 4. 15910 n 1. k=0 2n n−k − 2n n−k−1 k= 1 n 4 − 2 2n n 2n n 2n n 3 · 4n 2n n 2n n − (60n + 75)4n 6 Numerical Series and Inﬁnite Products n 2. k=0 n 3.

P) kp 2 3 ∞ (−1)k+1 2. 10 k=1 1 22n−1 π 2n |B2n |, = k 2n (2n)! ∞ (−1)k+1 4. k=1 ∞ 5. k=1 (−1)k+1 k=1 ∞ k=1 1 π2 = k2 6 1 (22n−1 − 1)π 2n |B2n | = k 2n (2n)! 1 (22n − 1)π 2n |B2n | = 2n (2k − 1) 2 · (2n)! ∞ 6. 1 = (1 − 21−p ) ζ(p) kp 1 π 2n+1 |E2n | = 2n+2 2n+1 (2k − 1) 2 (2n)! 234 Examples of numerical series ∞ (−1)k+1 1. k=1 ∞ 2. k=1 ∞ 3. k=0 ∞ 4. k=1 ∞ 5. k=1 ∞ 6. ∗ k=1 ∞ EU 1 π2 = 2 (2k − 1) 8 EU (−1)k =G (2k + 1)2 FI II 482 (−1)k+1 π3 = (2k − 1)3 32 EU 1 π4 = 4 (2k − 1) 96 EU (−1)k+1 5π 5 = (2k − 1)5 1536 EU (−1)k+1 7.