intersection indices

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$g, h$	positive integers.
…
$a\circ b$	intersection index of $a$ and $b$ , two cycles lying on a closed surface. $a\circ b=0$ if $a$ and $b$ do not intersect. Otherwise $a\circ b$ gets an additive contribution from every intersection point. This contribution is $1$ if the basis of the tangent vectors of the $a$ and $b$ cycles (§21.7(i)) at the point of intersection is positively oriented; otherwise it is $-1$ .
…

2: 21.7 Riemann Surfaces

… ►On this surface, we choose

2g

cycles (that is, closed oriented curves, each with at most a finite number of singular points)

a_{j}

b_{j}

j=1,2,\dots,g

, such that their intersection indices satisfy …

3: 4.37 Inverse Hyperbolic Functions

… ►In (4.37.3) the integration path may not intersect

\pm 1

. … ►The principal values (or principal branches) of the inverse

\sinh

\cosh

, and

\tanh

are obtained by introducing cuts in the

z

-plane as indicated in Figure 4.37.1(i)-(iii), and requiring the integration paths in (4.37.1)–(4.37.3) not to cross these cuts. …Each is two-valued on the corresponding cut(s), and each is real on the part of the real axis that remains after deleting the intersections with the corresponding cuts. … ►Except where indicated otherwise, it is assumed throughout the DLMF that the inverse hyperbolic functions assume their principal values. … ►This section also indicates conformal mappings, and surface plots for complex arguments. …

4: 4.23 Inverse Trigonometric Functions

… ►In (4.23.3) the integration path may not intersect

\pm i

. … ►The principal values (or principal branches) of the inverse sine, cosine, and tangent are obtained by introducing cuts in the

z

-plane as indicated in Figures 4.23.1(i) and 4.23.1(ii), and requiring the integration paths in (4.23.1)–(4.23.3) not to cross these cuts. …Each is two-valued on the corresponding cuts, and each is real on the part of the real axis that remains after deleting the intersections with the corresponding cuts. … ►Except where indicated otherwise, it is assumed throughout the DLMF that the inverse trigonometric functions assume their principal values. …

5: 3.5 Quadrature

… ►with saddle point at

t=1

, and when

c=1

the vertical path intersects the real axis at the saddle point. … ►Table 3.5.20 gives the results of applying the composite trapezoidal rule (3.5.2) with step size

h

;

n

indicates the number of function values in the rule that are larger than

10^{-15}

(we exploit the fact that the integrand is even). …

6: Mathematical Introduction

… ► ►►►

$\mathbb{C}$	complex plane (excluding infinity).
…
$\cap$	intersection.
…

… ►However, in many cases the coloring of the surface is chosen instead to indicate the quadrant of the plane to which the phase of the function belongs, thereby achieving a 4D effect. …

7: 4.2 Definitions

… ►where the integration path does not intersect the origin. … ►where the path does not intersect

(-\infty,0]

; see Figure 4.2.1. … ►However, in the absence of any indication to the contrary it is assumed that the definition is the closed one. … ►Unless indicated otherwise, it is assumed throughout the DLMF that a power assumes its principal value. …