…
►The main purpose of the present chapter is to extend these definitions and properties to complex arguments
.
►The main functions treated in this chapter are the logarithm
,
; the exponential
,
; the circular trigonometric (or just trigonometric) functions
,
,
,
,
,
; the inverse trigonometric functions
,
, etc.
; the hyperbolic trigonometric (or just hyperbolic) functions
,
,
,
,
,
; the inverse hyperbolic functions
,
, etc.
►Sometimes in the literature the meanings of
and
are interchanged; similarly for
and
, etc.
…
for
and
for
.
…
►For the Hermite polynomial
see §
18.3.
►
7.10.2
►
7.10.3
.
►
►
…
►
4.9.2
►valid when
; see Figure
4.23.1(i).
…
►For
,
►
►
…
…
►
12.4.1
►
12.4.2
►where the initial values are given by (
12.2.6)–(
12.2.9), and
and
are the even and odd solutions of (
12.2.2) given by
…
►
12.4.4
…
►These series converge for all values of
.
…
►For
and
,
…
►Jacobi–Anger expansions: for
,
…
►
►
►
…
►
4.25.3
►valid when
lies in the open cut plane shown in Figure
4.23.1(i).
►
4.25.4
►valid when
lies in the open cut plane shown in Figure
4.23.1(ii).
…valid when
lies in the open cut plane shown in Figure
4.23.1(iv).
…