Rational Zeta Series - Half-integer Power Series

Half-integer Power Series

Similar series may be obtained by exploring the Hurwitz zeta function at half-integer values. Thus, for example, one has

\sum_{k=0}^\infty \frac {\zeta(k+n+2)-1}{2^k} {{n+k+1} \choose {n+1}}=\left(2^{n+2}-1\right)\zeta(n+2)-1

Read more about this topic:  Rational Zeta Series

Famous quotes containing the words power and/or series:

    “There are times when they seem so small! And then again, although they never seem large, there is a vastness behind them, a past of indefinite complexity and marvel, an amazing power of absorbing and assimilating, which forces one to suspect some power in the race so different from our own that one cannot understand that power. And ... whatever doubts or vexations one has in Japan, it is only necessary to ask oneself: “Well, who are the best people to live with?””
    —Lafcadio Hearn (1850–1904)

    “Rosalynn said, “Jimmy, if we could only get Prime Minister Begin and President Sadat up here on this mountain for a few days, I believe they might consider how they could prevent another war between their countries.” That gave me the idea, and a few weeks later, I invited both men to join me for a series of private talks. In September 1978, they both came to Camp David.”
    —Jimmy Carter (James Earl Carter, Jr.)