Lines Matching full:functions

1 [section:hankel Hankel Functions]
2 [section:cyl_hankel Cyclic Hankel Functions]
21 The functions __cyl_hankel_1 and __cyl_hankel_2 return the result of the
22 [@http://dlmf.nist.gov/10.2#P3 Hankel functions] of the first and second kind respectively:
32 The return type of these functions is computed using the __arg_promotion_rules
33 when T1 and T2 are different types.  The functions are also optimised for the
38 Note that while the arguments to these functions are real values, the results are complex.
39 That means that the functions can only be instantiated on types `float`, `double` and `long double`.
40 The functions have also been extended to operate over the whole range of ['v] and ['x] 
45 These functions are generally more efficient than two separate calls to the underlying Bessel
46 functions as internally Bessel J and Y can be computed simultaneously.
51 on the Bessel functions upon which these are based.
61 [@http://functions.wolfram.com/Bessel-TypeFunctions/BesselJ/16/01/01/ [equation hankel1]]
63 [@http://functions.wolfram.com/Bessel-TypeFunctions/BesselY/16/01/01/ [equation hankel2]]
65 [@http://functions.wolfram.com/Bessel-TypeFunctions/BesselY/16/01/01/ [equation hankel3]]
67 Otherwise the implementation is trivially in terms of the Bessel J and Y functions.
69 Note however, that the Hankel functions compute the Bessel J and Y functions simultaneously,
74 [endsect] [/section:cyl_hankel Cyclic Hankel Functions]
76 [section:sph_hankel Spherical Hankel Functions]
95 The functions __sph_hankel_1 and __sph_hankel_2 return the result of the
96 [@http://dlmf.nist.gov/10.47#P1 spherical Hankel functions] of the first and second kind respective…
102 The return type of these functions is computed using the __arg_promotion_rules
103 when T1 and T2 are different types.  The functions are also optimised for the
108 Note that while the arguments to these functions are real values, the results are complex.
109 That means that the functions can only be instantiated on types `float`, `double` and `long double`.
110 The functions have also been extended to operate over the whole range of ['v] and ['x] 
116 on the Bessel functions upon which these are based.
124 These functions are trivially implemented in terms of __cyl_hankel_1 and __cyl_hankel_2.
126 [endsect] [/section:sph_hankel Spherical Hankel Functions]
128 [endsect] [/section:hankel Hankel Functions]