update docs and add news

heltonmc · heltonmc · commit 08b1c53f230b · 2022-09-19T13:00:24.000-04:00
diff --git a/NEWS.md b/NEWS.md
@@ -12,7 +12,8 @@ For bug fixes, performance enhancements, or fixes to unexported functions we wil
 
 ### Added
  - Add more optimized methods for Float32 calculations that are faster ([PR #43](https://github.com/JuliaMath/Bessels.jl/pull/43))
- - Add methods for computing modified spherical bessel function of second ([PR #46](https://github.com/JuliaMath/Bessels.jl/pull/46) and ([PR #47](https://github.com/JuliaMath/Bessels.jl/pull/47))) currently unexported closes ([Issue #25](https://github.com/JuliaMath/Bessels.jl/issues/25))
+ - Add methods for computing modified spherical bessel function of second ([PR #46](https://github.com/JuliaMath/Bessels.jl/pull/46) contributed by @cgeoga and first ([PR #47](https://github.com/JuliaMath/Bessels.jl/pull/47))) kind. These functions are currently not exported. Closes ([Issue #25](https://github.com/JuliaMath/Bessels.jl/issues/25))
+ - Asymptotic expansion for x >> nu was added ([PR #48](https://github.com/JuliaMath/Bessels.jl/pull/48)) that decreases computation time for large arguments. Contributed by @cgeoga
 
 ### Fixed
  - Reduce compile time and time to first call of besselj and bessely ([PR #42](https://github.com/JuliaMath/Bessels.jl/pull/42))
diff --git a/src/besselk.jl b/src/besselk.jl
@@ -160,6 +160,7 @@ end
 #
 #    The identities are computed by calling the `besseli_positive_args(nu, x)` function which computes K_{ν}(x)
 #    for positive arguments and orders. For large orders, Debye's uniform asymptotic expansions are used.
+#    For large arguments x >> nu, large argument expansion is used [9].
 #    For small value and when nu > ~x the power series is used. The rest of the values are computed using slightly different methods.
 #    The power series for besseli is modified to give both I_{v} and I_{v-1} where the ratio K_{v+1} / K_{v} is computed using continued fractions [8].
 #    The wronskian connection formula is then used to compute K_v.
@@ -178,6 +179,7 @@ end
 #     arXiv preprint arXiv:2201.00090 (2022).
 # [8] Cuyt, A. A., Petersen, V., Verdonk, B., Waadeland, H., & Jones, W. B. (2008). 
 #     Handbook of continued fractions for special functions. Springer Science & Business Media.
+# [9] http://dlmf.nist.gov/10.40.E2
 #
 
 """

Original file line number	Diff line number	Diff line change
`@@ -160,6 +160,7 @@ end`
`160`	`160`	`#`
`161`	`161`	# The identities are computed by calling the `besseli_positive_args(nu, x)` function which computes K_{ν}(x)
`162`	`162`	`# for positive arguments and orders. For large orders, Debye's uniform asymptotic expansions are used.`
	`163`	`+# For large arguments x >> nu, large argument expansion is used [9].`
`163`	`164`	`# For small value and when nu > ~x the power series is used. The rest of the values are computed using slightly different methods.`
`164`	`165`	`# The power series for besseli is modified to give both I_{v} and I_{v-1} where the ratio K_{v+1} / K_{v} is computed using continued fractions [8].`
`165`	`166`	`# The wronskian connection formula is then used to compute K_v.`
`@@ -178,6 +179,7 @@ end`
`178`	`179`	`# arXiv preprint arXiv:2201.00090 (2022).`
`179`	`180`	`# [8] Cuyt, A. A., Petersen, V., Verdonk, B., Waadeland, H., & Jones, W. B. (2008).`
`180`	`181`	`# Handbook of continued fractions for special functions. Springer Science & Business Media.`
	`182`	`+# [9] http://dlmf.nist.gov/10.40.E2`
`181`	`183`	`#`
`182`	`184`
`183`	`185`	`"""`