@article{oai:ipsj.ixsq.nii.ac.jp:00070147,
 author = {吉田, 年雄 and Toshio, Yoshida},
 issue = {8},
 journal = {情報処理学会論文誌},
 month = {Aug},
 note = {本論文では，$x M^{2}_{
u}(x)=x\{J_{
u}^{2}(x)+Y_{
u}^{2}(x)\}$について，変数$x$が大きい場合の能率的な計算法を提案している．ここで，$J_{
u}(x)$および$Y_{
u}(x)$はベッセル関数である．$xM_{
u}^{2}(x)$は$xM_{
u}^{2}(x)=(1/\sqrt{t})M_{
u}^{2}(1/\sqrt{t})=f_{
u}(t)$のように書くことができ，$f_{
u}(t)$は，微分方程式$8t^{3}f_{
u}'''(t)+36t^{2}f_{
u}''(t)+\{(26-8
u^{2})t+8\}f_{
u}'(t)-(4
u^{2}-1)f_{
u}(t)=0$を満足する．上式に$\tau$法を適用すると，$f_{
u}(t)$の近似式が求められ，式の変形や工夫を行うことより，能率的な計算式が得られる．, In this paper, we propose an efficient numerical method for $x M^{2}_{
u}(x)=x\{J_{
u}^{2}(x)+Y_{
u}^{2}(x)\}$ with large argument $x$, where $J_{
u}(x)$ and $Y_{
u}(x)$ are Bessel functions. The function $xM_{
u}^{2}(x)$ is written as $xM_{
u}^{2}(x)=(1/\sqrt{t})M_{
u}^{2}(1/\sqrt{t}))=f_{
u}(t)$, where $f_{
u}(t)$ satisfies the differential equation $8t^{3}f_{
u}'''(t)+36t^{2}f_{
u}''(t)+\{(26-8
u^{2})t+8\}f_{
u}'(t)-(4
u^{2}-1)f_{
u}(t)=0$. Applying the $\tau$-method to the above equation, the approximation to $f_{
u}(t)$ is obtained.},
 pages = {1394--1401},
 title = {{\boldmath $\tau$}法による{\boldmath$x$}が大きい場合の{\boldmath$x\{J_{\nu}^{2}(x)+Y_{\nu}^{2}(x)\}$}の数値計算},
 volume = {51},
 year = {2010}
}