漸化式を用いる複素変数のベッセル関数I_n(z)の数値計算

概要

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The recurrence techniques are useful for computing the value of I_n(z) or J_n(z) with complex argument as well as that with real argument. The approximate value of I_n(z) is given by I_n(z)≃(e^zG_m(Z))/(?^^m__<k=0>ε_kG_k(z)), ε_k=[Numerical fomular], where G_<m+1>(z)=0, G_m(z)=α≠0(α:an arbitrary constant) and then G_<m-1>(z), G_<m-2>(z), ..., G_n(z), …, G_1(z), G_0(z) are the values obtained by the successive application of the recurrence relation G_<k-1>(z)=((2k)/z)G_k(z)+G_<k+1>(z). The larger the value of the integer m, the higher the accuracy in the approximate value of I_n(z). However, in order to compute the value of I_n(z) with a given accuracy as efficiently as possible, the value of m must be chosen minimum. In this paper is obtained for a given value of z the minimum value M of m in the computation of I_n(z) with a desired accuracy. Also for convenience of the actual computation, we could give a simple function of R_e(z) and I_m(z)for M.
一般社団法人情報処理学会の論文
1973-01-15