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

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Series involving Reciprocals of Powers of Positive Integers

$19.14$: Newton-Mercator Series for $\ln 2$
$19.15$: 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 Even Powers of Integers Alternating in Sign
$19.38$: Sum of Reciprocals of Odd Powers of Odd Integers Alternating in Sign