# indices differing by an integer

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## 11—13 of 13 matching pages

##### 11: 21.7 Riemann Surfaces

*cycles*(that is, closed oriented curves, each with at most a finite number of singular points) ${a}_{j}$, ${b}_{j}$, $j=1,2,\mathrm{\dots},g$, such that their

*intersection indices*satisfy … ►Next, define an isomorphism $\mathit{\eta}$ which maps every subset $T$ of $B$ with an even number of elements to a $2g$-dimensional vector $\mathit{\eta}(T)$ with elements either $0$ or $\frac{1}{2}$. … ►

##### 12: Errata

A sentence was added at the end of the subsection indicating that for generalizations, see Cohl and Costas-Santos (2020).

In Equation (1.13.4), the determinant form of the two-argument Wronskian

was added as an equality. In ¶Wronskian (in §1.13(i)), immediately below Equation (1.13.4), a sentence was added indicating that in general the $n$-argument Wronskian is given by $\mathcal{W}\left\{{w}_{1}(z),\mathrm{\dots},{w}_{n}(z)\right\}=det\left[{w}_{k}^{(j-1)}(z)\right]$, where $1\le j,k\le n$. Immediately below Equation (1.13.4), a sentence was added giving the definition of the $n$-argument Wronskian. It is explained just above (1.13.5) that this equation is often referred to as Abel’s identity. Immediately below Equation (1.13.5), a sentence was added explaining how it generalizes for $n$th-order differential equations. A reference to Ince (1926, §5.2) was added.

the previous constraint $a\ne 0,-1,-2,\mathrm{\dots},$ was removed. A clarification regarding the correct constraints for Lerch’s transcendent $\mathrm{\Phi}(z,s,a)$ has been added in the text immediately below. In particular, it is now stated that if $s$ is not an integer then $$; if $s$ is a positive integer then $a\ne 0,-1,-2,\mathrm{\dots}$; if $s$ is a non-positive integer then $a$ can be any complex number.

*Suggested by Tom Koornwinder.*

An addition was made to the Software Index to reflect a multiple precision (MP) package written in C++ which uses a variety of different MP interfaces. See Kormanyos (2011).