The Von Staudt–Clausen theorem is a result in the field of number theory, particularly concerning the theory of continued fractions and the approximation of numbers. The theorem provides a way to express a specific class of numbers, notably the values of certain mathematical constants, as a sum involving continued fractions.
Articles by others on the same topic
For , the von Staudt-Clausen theorem statesConsequently the positive denominator of the Bernoulli number in lowest terms is exactly the squarefree product of the primes satisfying . This gives its denominator without computing its numerator.[ref]
For , the relevant primes are . Their reciprocals sum to , and , so the displayed expression is . The theorem concerns even positive indices; is handled separately. It explains the recurring small prime factors in denominators of formulas for sums of powers.