§17.1 Special Notation
…
►
►The main
functions treated in this chapter are the basic
hypergeometric (or
-
hypergeometric)
function
, the bilateral basic
hypergeometric (or bilateral
-
hypergeometric)
function
, and the
-analogs of the Appell
functions
,
,
, and
.
►Another
function notation used is the “idem”
function:
…
§11.9 Lommel Functions
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►
…
►
§11.9(ii) Expansions in Series of Bessel Functions
…
►For collections of integral
representations and integrals see
Apelblat (1983, §12.17),
Babister (1967, p. 85),
Erdélyi et al. (1954a, §§4.19 and 5.17),
Gradshteyn and Ryzhik (2000, §6.86),
Marichev (1983, p. 193),
Oberhettinger (1972, pp. 127–128, 168–169, and 188–189),
Oberhettinger (1974, §§1.12 and 2.7),
Oberhettinger (1990, pp. 105–106 and 191–192),
Oberhettinger and Badii (1973, §2.14),
Prudnikov et al. (1990, §§1.6 and 2.9),
Prudnikov et al. (1992a, §3.34), and
Prudnikov et al. (1992b, §3.32).
…
►(For other notation see
Notation for the Special Functions.)
►
►The main
functions treated in this chapter are the Airy
functions
and
, and the Scorer
functions
and
(also known as inhomogeneous Airy
functions).
►Other notations that have been used are as follows:
and
for
and
(
Jeffreys (1928), later changed to
and
);
,
(
Fock (1945));
(
Szegő (1967, §1.81));
,
(
Tumarkin (1959)).
…
►(For other notation see
Notation for the Special Functions.)
►
►The main
functions treated in this chapter are
,
,
, and the polynomial
.
…Sometimes the parameters are suppressed.
§5.15 Polygamma Functions
►The
functions
,
, are called the
polygamma functions.
In particular,
is the
trigamma function;
,
,
are the
tetra-, penta-, and
hexagamma functions respectively.
Most properties of these
functions follow straightforwardly by differentiation of properties of the psi
function.
…
►For
see §
24.2(i).
…