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node_modules/tstl/numeric/special_math/bessels.js

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+"use strict";
+Object.defineProperty(exports, "__esModule", { value: true });
+exports.cyl_bessel_k = exports.cyl_bessel_i = exports.sph_neumann = exports.sph_bessel = exports.cyl_neumann = exports.cyl_bessel_j = void 0;
+//================================================================
+/**
+ * @packageDocumentation
+ * @module std
+ */
+//================================================================
+var MathUtil_1 = require("../../internal/numeric/MathUtil");
+var InvalidArgument_1 = require("../../exception/InvalidArgument");
+var gamma_1 = require("./gamma");
+var INFINITY = 100; // (1 / 30!) is nearby 0.
+/*================================================================
+    ORIGINAL FUNCTIONS
+        - CYLINDRICAL
+        - SPHERICAL
+==================================================================
+    FIRST KIND
+--------------------------------------------------------------- */
+/**
+ * Bessel function of the 1st kind.
+ *
+ * @reference https://en.wikipedia.org/wiki/Bessel_function#Bessel_functions_of_the_first_kind:_J.CE.B1
+ */
+function cyl_bessel_j(n, x) {
+    // VALIDATION
+    if (x < 0 && Math.floor(n) !== n)
+        throw new InvalidArgument_1.InvalidArgument("Error on std.cyl_bessel_j(): n must be integer when x is negative -> (n = ".concat(n, ", x = ").concat(x, ")."));
+    else if (x === 0 && n !== 0)
+        throw new InvalidArgument_1.InvalidArgument("Error on std.cyl_bessel_j(): n must be zero when x is zero -> (n = ".concat(n, ", x = ").concat(x, ")."));
+    // COMPUTATION
+    if (n === Math.floor(n))
+        return _J_int(n, x);
+    else
+        return _J_positive(n, x);
+}
+exports.cyl_bessel_j = cyl_bessel_j;
+/**
+ * Bessel function of the 2nd kind.
+ *
+ * @reference https://en.wikipedia.org/wiki/Bessel_function#Bessel_functions_of_the_second_kind:_Y.CE.B1
+ */
+function cyl_neumann(v, x) {
+    if (x <= 0)
+        throw new InvalidArgument_1.InvalidArgument("Error on std.cyl_neumann(): x must be greater than zero -> (x = ".concat(x, ")."));
+    var numerator = cyl_bessel_j(v, x) * Math.cos(v * Math.PI) - cyl_bessel_j(-v, x);
+    var denominator = Math.sin(v * Math.PI);
+    return numerator / denominator;
+}
+exports.cyl_neumann = cyl_neumann;
+function _J_int(n, x) {
+    if (n < 0)
+        return Math.pow(-1, n) * _J_positive(-n, x);
+    else
+        return _J_positive(n, x);
+}
+function _J_positive(v, x) {
+    var sigma = MathUtil_1.MathUtil.sigma(function (k) {
+        var ret = Math.pow(-1, k) * Math.pow(x / 2, v + 2 * k);
+        ret /= MathUtil_1.MathUtil.factorial(k) * (0, gamma_1.tgamma)(v + k + 1);
+        return ret;
+    }, 0, INFINITY);
+    return sigma;
+}
+/* ---------------------------------------------------------------
+    SPHERICAL
+--------------------------------------------------------------- */
+/**
+ * Spherical Bessel function of the 1st kind.
+ *
+ * @reference https://en.wikipedia.org/wiki/Bessel_function#Spherical_Bessel_functions:_jn.2C_yn
+ */
+function sph_bessel(n, x) {
+    return Math.sqrt(Math.PI / (2 * x)) * cyl_bessel_j(n + 0.5, x);
+}
+exports.sph_bessel = sph_bessel;
+/**
+ * Spherical Bessel function of the 2nd kind.
+ *
+ * @reference https://en.wikipedia.org/wiki/Bessel_function#Spherical_Bessel_functions:_jn.2C_yn
+ */
+function sph_neumann(n, x) {
+    var ret = Math.sqrt(Math.PI / (2 * x));
+    ret *= cyl_neumann(n + 0.5, x);
+    return ret;
+}
+exports.sph_neumann = sph_neumann;
+/*================================================================
+    REQGULAR MODIFIED
+        - FIRST KIND
+        - SECOND KIND
+==================================================================
+    FIRST KIND
+--------------------------------------------------------------- */
+/**
+ * Modified cylindrical Bessel function of the 1st kind.
+ *
+ * @reference https://en.wikipedia.org/wiki/Bessel_function#Modified_Bessel_functions:_I.CE.B1_.2C_K.CE.B1
+ */
+function cyl_bessel_i(n, x) {
+    // VALIDATION
+    if (x < 0 && Math.floor(n) !== n)
+        throw new InvalidArgument_1.InvalidArgument("Error on std.cyl_bessel_i(): n must be integer when x is negative -> (n = ".concat(n, ", x = ").concat(x, ")."));
+    else if (x === 0 && n !== 0)
+        throw new InvalidArgument_1.InvalidArgument("Error on std.cyl_bessel_i(): n must be zero when x is zero -> (n = ".concat(n, ", x = ").concat(x, ")."));
+    // COMPUTATION
+    if (n === 0.5)
+        return Math.sqrt(2.0 / (Math.PI * x)) * Math.sinh(x);
+    else
+        return _Bessel_i(n, x);
+}
+exports.cyl_bessel_i = cyl_bessel_i;
+function _Bessel_i(v, x) {
+    return MathUtil_1.MathUtil.sigma(function (k) {
+        var numerator = Math.pow(x / 2, v + 2 * k);
+        var denominator = MathUtil_1.MathUtil.factorial(k) * (0, gamma_1.tgamma)(v + k + 1);
+        return numerator / denominator;
+    }, 0, INFINITY);
+}
+/* ---------------------------------------------------------------
+    SECOND KIND
+--------------------------------------------------------------- */
+/**
+ * Modified cylindrical Bessel function of the 2nd kind.
+ *
+ * @reference https://en.wikipedia.org/wiki/Bessel_function#Modified_Bessel_functions:_I.CE.B1_.2C_K.CE.B1
+ */
+function cyl_bessel_k(n, x) {
+    if (x <= 0)
+        throw new InvalidArgument_1.InvalidArgument("Error on std.cyl_bessel_k(): requires x > 0 -> (x = ".concat(x, ")."));
+    return _Bessel_k(n, x);
+}
+exports.cyl_bessel_k = cyl_bessel_k;
+function _Bessel_k(v, z) {
+    var ret = Math.PI / 2;
+    ret *= cyl_bessel_i(-v, z) - cyl_bessel_i(v, z);
+    ret /= Math.sin(v * Math.PI);
+    return ret;
+}
+//# sourceMappingURL=bessels.js.map