Bessel functions and Hankel functions
(0.015 seconds)
1—10 of 66 matching pages
1: 10.1 Special Notation
…
►The main functions treated in this chapter are the Bessel functions
, ; Hankel functions
, ; modified Bessel functions
, ; spherical Bessel functions
, , , ; modified spherical Bessel functions
, , ; Kelvin functions
, , , .
…
►For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).
2: 10.76 Approximations
…
►
§10.76(ii) Bessel Functions, Hankel Functions, and Modified Bessel Functions
…3: 10.46 Generalized and Incomplete Bessel Functions; Mittag-Leffler Function
…
►For incomplete modified Bessel functions and Hankel functions, including applications, see Cicchetti and Faraone (2004).
4: 10.4 Connection Formulas
5: 10.74 Methods of Computation
…
►The power-series expansions given in §§10.2 and 10.8, together with the connection formulas of §10.4, can be used to compute the Bessel and Hankel functions when the argument or is sufficiently small in absolute value.
…
►For the function
, for example, can always be computed in a stable manner in the sector by integrating along rays towards the origin.
…
►For evaluation of the Hankel functions
and for complex values of and based on the integral representations (10.9.18) see Remenets (1973).
…
►
►
§10.74(vi) Zeros and Associated Values
…6: 10.2 Definitions
…
►
§10.2(i) Bessel’s Equation
… ►Bessel Functions of the Third Kind (Hankel Functions)
… ►
10.2.5
…
►
10.2.6
…
►
Branch Conventions
…7: 10.5 Wronskians and Cross-Products
8: 10.16 Relations to Other Functions
9: 10.77 Software
…
►