…
โบFor the confluent hypergeometric
functions
,
,
, and the Whittaker
functions
and
, see §§
13.2(i) and
13.14(i).
โบ
8.5.1
.
โบ
8.5.2
โบ
8.5.3
…
…
โบStandard solutions are:
โบ
13.14.2
โบ
13.14.3
…
โบ
13.14.5
…
โบThe
principal branches correspond to the principal branches of the
functions
and
on the right-hand sides of the equations (
13.14.2) and (
13.14.3); compare §
4.2(i).
…
…
โบThe integral representations (
13.4.1) and (
13.4.4) can be used to compute the
Kummer functions, and (
13.16.1) and (
13.16.5) for the Whittaker
functions.
In
Allasia and Besenghi (1991) and
Allasia and Besenghi (1987a) the high accuracy of the trapezoidal rule for the computation of
Kummer functions is described.
…
โบ
13.29.6
…
…
โบ
18.11.2
โบFor the confluent hypergeometric
functions
and
, see §
13.2(i), and for the Whittaker
functions
and
see §
13.14(i).
…
โบ
18.11.3
โบ
18.11.4
…
…
โบ
9.10.14
.
…
โบFor the confluent hypergeometric
function
and the incomplete gamma
function
see §§
13.1,
13.2, and
8.2(i).
…
…
โบFor the confluent hypergeometric
function
and the generalized hypergeometric
function
, the Laguerre polynomial
and the Whittaker
function
see §
16.2(ii), §
16.2(iv), (
18.5.12), and (
13.14.3), respectively.
โบ
18.34.1
…