Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 19/Series involving Reciprocals of Powers of Positive Integers

Series involving Reciprocals of Powers of Positive Integers

 * $19.14$: Alternating Harmonic Series sums to $\ln 2$


 * $19.15$: Leibniz's Formula for $\pi$


 * $19.16$: Sum of Sequence of Reciprocals of $3 n + 1$ Alternating in Sign


 * $19.17$: Sum of Sequence of Reciprocals of $4 n + 1$ Alternating in Sign


 * $19.18$: Sum of Sequence of Reciprocals of $3 n + 2$ Alternating in Sign


 * $19.19$: Basel Problem


 * $19.20$: Riemann Zeta Function of $4$


 * $19.21$: Riemann Zeta Function of $6$


 * $19.22$: Sum of Reciprocals of Squares Alternating in Sign


 * $19.23$: Sum of Reciprocals of Fourth Powers Alternating in Sign


 * $19.24$: Sum of Reciprocals of Sixth Powers Alternating in Sign


 * $19.25$: Sum of Reciprocals of Squares of Odd Integers


 * $19.26$: Sum of Reciprocals of Fourth Powers of Odd Integers


 * $19.27$: Sum of Reciprocals of Sixth Powers of Odd Integers


 * $19.28$: Sum of Reciprocals of Cubes of Odd Integers Alternating in Sign


 * $19.29$: Sum of Reciprocals of Cubes of Odd Integers Alternating in Sign in Pairs


 * $19.30$: Sum of Sequence of Products of Consecutive Odd Reciprocals: Corollary


 * $19.31$: Sum of Sequence of Products of Consecutive Odd and Consecutive Even Reciprocals: Corollary


 * $19.32$: Sum of Sequence of Products of Squares of Consecutive Odd Reciprocals


 * $19.33$: Sum of Sequence of Products of Squares of 3 Consecutive Reciprocals


 * $19.34$: Definite Integral from $0$ to $1$ of $\dfrac {u^{a - 1} } {1 + u^d}$


 * $19.35$: Riemann Zeta Function at Even Integers


 * $19.36$: Sum of Reciprocals of Even Powers of Odd Integers


 * $19.37$: Sum of Reciprocals of Powers of Integers Alternating in Sign


 * $19.38$: Sum of Reciprocals of Odd Powers of Odd Integers Alternating in Sign