# Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 21

## Murray R. Spiegel: Mathematical Handbook of Formulas and Tables: Chapter 21

Published $\text {1968}$.

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## $21 \quad$ Bernoulli and Euler Numbers

### Definition of Bernoulli Numbers

$21.1$: Bernoulli Numbers: Archaic Form: Definition 1
$21.2$: Bernoulli Numbers: Archaic Form: Definition 2

### Definition of Euler Numbers

$21.3$: Euler Numbers: Alternative Form: Definition 1
$21.4$: Euler Numbers: Alternative Form: Definition 2

### Table of First Few Bernoulli and Euler Numbers

Bernoulli Numbers: Archaic Form: Sequence
Euler Numbers: Alternative Form: Sequence

### Relationships of Bernoulli and Euler Numbers

$21.5$: Sum of Bernoulli Numbers by Power of Two and Binomial Coefficient
$21.6$: Sum of Euler Numbers by Binomial Coefficient
$21.7$: Bernoulli Number in terms of Euler Numbers

### Series involving Bernoulli and Euler Numbers

$21.8$: Riemann Zeta Function at Even Integers: Corollary
$21.9$: Sum of Reciprocals of Even Powers of Odd Integers: Corollary
$21.10$: Sum of Reciprocals of Powers of Integers Alternating in Sign: Corollary
$21.11$: Sum of Reciprocals of Odd Powers of Odd Integers Alternating in Sign: Corollary

### Asymptotic Formula for Bernoulli Numbers

$21.12$: Asymptotic Formula for Bernoulli Numbers

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