Concrete Mathematics

Ronald L. Graham, D. E. K., Oren Patashnik, C. M. A. F. f. C. S., & Bernoulli numbers, I. 9. (1994). Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley.

Type

Book chapter

Intellectual base

Textbook

Year

1994

ISBN

9780201558029

Link

https://openlibrary.org/books/OL1429049Mmatched

Cited from

accounting_auditing

Cited by

3 citations across 3 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Double Counting
  • The error lives at the boundary between buckets: an item belonging to both A and B is counted once when A is totalled and again when B is totalled, so the system reports A + B instead of A + B − (A ∩ B).

    This sourceStates and applies the inclusion-exclusion principle |A ∪ B| = |A| + |B| − |A ∩ B| and its higher-order generalization. (Print textbook, ISBN 0-201-55802-5.)

Domain-specific

• Bernoulli number
  • … gives \(B_0=1\), \(B_1=-\tfrac12\), \(B_2=\tfrac16\), and \(B_4=-\tfrac1{30}\), while the odd values beyond \(B_1\) vanish. to Euler-Maclaurin summation uses even Bernoulli numbers as coefficients of endpoint-derivative corrections when approximating a finite sum by an integral. demonstrates that continuity.
• Derangement
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Verification

This reference passed the adversarial substantiation pipeline: it was checked to exist and to support the claim it is attached to. See how references were verified.

Registry ID ref:2db154fea3c2 · see in the full table