136 lines
11 KiB
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136 lines
11 KiB
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<title>std::sph_bessel, std::sph_besself, std::sph_bessell</title>
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>sph_bessel, <span style="font-size:0.7em; line-height:130%">std::</span>sph_besself, <span style="font-size:0.7em; line-height:130%">std::</span>sph_bessell</h1>
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<div id="contentSub"><span class="subpages">< <a href="cpp.html">cpp</a>‎ | <a href="cpp-numeric.html">numeric</a>‎ | <a href="cpp-numeric-special_functions.html">special functions</a></span></div>
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<div>定义于头文件 <code><a href="cpp-header-cmath.html"><cmath></a></code></div>
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<td></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span> sph_bessel <span class="br0">(</span> <span class="kw4">unsigned</span> n, <span class="kw4">double</span> x <span class="br0">)</span><span class="sy4">;</span><br /></span>
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<p><span class="kw4">float</span> sph_bessel <span class="br0">(</span> <span class="kw4">unsigned</span> n, <span class="kw4">float</span> x <span class="br0">)</span><span class="sy4">;</span><br />
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<span class="kw4">long</span> <span class="kw4">double</span> sph_bessel <span class="br0">(</span> <span class="kw4">unsigned</span> n, <span class="kw4">long</span> <span class="kw4">double</span> x <span class="br0">)</span><span class="sy4">;</span><br />
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<span class="kw4">float</span> sph_besself<span class="br0">(</span> <span class="kw4">unsigned</span> n, <span class="kw4">float</span> x <span class="br0">)</span><span class="sy4">;</span><br /></p>
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<span class="kw4">long</span> <span class="kw4">double</span> sph_bessell<span class="br0">(</span> <span class="kw4">unsigned</span> n, <span class="kw4">long</span> <span class="kw4">double</span> x <span class="br0">)</span><span class="sy4">;</span></div>
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<td>(1)</td>
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<td><span class="t-mark-rev t-since-cxx17">(C++17 起)</span></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span> sph_bessel<span class="br0">(</span> <span class="kw4">unsigned</span> n, IntegralType x <span class="br0">)</span><span class="sy4">;</span></span></div>
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<td>(2)</td>
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<td><span class="t-mark-rev t-since-cxx17">(C++17 起)</span></td>
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<div class="t-li1"><span class="t-li">1)</span> 计算 <code>n</code> 和 <code>x</code> 的<a href="https://en.wikipedia.org/wiki/Bessel_function#Spherical_Bessel_functions:_jn.2C_yn" class="extiw" title="enwiki:Bessel function">第一类球贝塞尔函数</a>。</div>
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<div class="t-li1"><span class="t-li">2)</span> 接受任意<a href="cpp-types-is_integral.html">整数类型</a>参数的重载集或函数模板。等价于将参数转型到 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> 后的 <span class="t-v">(1)</span> 。</div>
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<h3><span class="mw-headline" id=".E5.8F.82.E6.95.B0">参数</span></h3>
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<table class="t-par-begin">
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<td>n</td>
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<td>-</td>
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<td>函数的阶数</td>
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<tr class="t-par">
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<td>x</td>
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<td>-</td>
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<td>函数的参数</td>
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</tr>
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</table>
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<h3><span class="mw-headline" id=".E8.BF.94.E5.9B.9E.E5.80.BC">返回值</span></h3>
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<p>若无错误发生，则返回 <code>n</code> 和 <code>x</code> 的第一类球贝塞尔函数，即 <span class="texhtml" style="white-space: nowrap;">j<span class="t-su t-su-b"><br />
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n</span>(x) = (π/2x)<span class="t-su">1/2<br /></span>J<span class="t-su t-su-b"><br />
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n+1/2</span>(x)</span> ，其中 <span class="texhtml" style="white-space: nowrap;">J<span class="t-su t-su-b"><br />
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n</span>(x)</span> 为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-numeric-special_math-cyl_bessel_j.html"><span class="kw1408">std::<span class="me2">cyl_bessel_j</span></span></a><span class="br0">(</span>n,x<span class="br0">)</span></span></span> 且 <span class="texhtml" style="white-space: nowrap;">x≥0</span></p>
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<h3><span class="mw-headline" id=".E9.94.99.E8.AF.AF.E5.A4.84.E7.90.86">错误处理</span></h3>
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<p>可能报告 <a href="cpp-numeric-math-math_errhandling.html"><tt>math_errhandling</tt></a> 中指定的错误</p>
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<ul>
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<li>若参数是 NaN ，则返回 NaN 且不报告定义域错误</li>
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<li>若 <span class="texhtml" style="white-space: nowrap;">n>=128</span> ，则行为是实现定义的</li>
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</ul>
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<h3><span class="mw-headline" id=".E6.B3.A8.E8.A7.A3">注解</span></h3>
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<p>不支持 C++17 ，但支持 <a href="cpp-experimental-special_functions.html">ISO 29124:2010</a> 的实现会提供此函数，若实现定义了 <code>__STDCPP_MATH_SPEC_FUNCS__</code> 为至少 201003L 的值，且用户在包含任何标准库头文件前定义了 <code>__STDCPP_WANT_MATH_SPEC_FUNCS__</code> 。</p>
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<p>不支持 ISO 29124:2010 但支持 TR 19768:2007 (TR1) 的实现，在头文件 <code>tr1/cmath</code> 及命名空间 <code>std::tr1</code> 中提供此函数。</p>
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<p>此函数的一种实现亦<a rel="nofollow" class="external text" href="http://www.boost.org/doc/libs/1_62_0/libs/math/doc/html/math_toolkit/bessel/sph_bessel.html">可用于 boost.math</a></p>
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<h3><span class="mw-headline" id=".E5.8F.82.E9.98.85">参阅</span></h3>
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<div class="t-example">
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<div class="t-example-live-link"></div>
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<div dir="ltr" class="mw-geshi" style="text-align: left;">
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<div class="cpp source-cpp">
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<pre class="de1"><span class="co2">#include <cmath></span>
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<span class="co2">#include <iostream></span>
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<span class="kw4">int</span> main<span class="br0">(</span><span class="br0">)</span>
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<span class="br0">{</span>
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<span class="co1">// 对 n == 1 的点检查</span>
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<span class="kw4">double</span> x <span class="sy1">=</span> <span class="nu16">1.2345</span><span class="sy4">;</span>
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<a href="cpp-io-cout.html"><span class="kw1758">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"j_1("</span> <span class="sy1"><<</span> x <span class="sy1"><<</span> <span class="st0">") = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-special_math-sph_bessel.html"><span class="kw1441">std::<span class="me2">sph_bessel</span></span></a><span class="br0">(</span><span class="nu0">1</span>, x<span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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<span class="co1">// 对 j_1 的准确解</span>
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<a href="cpp-io-cout.html"><span class="kw1758">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <span class="st0">"(sin x)/x^2 - (cos x)/x = "</span> <span class="sy1"><<</span> <a href="cpp-numeric-math-sin.html"><span class="kw1333">std::<span class="me2">sin</span></span></a><span class="br0">(</span>x<span class="br0">)</span><span class="sy2">/</span><span class="br0">(</span>x<span class="sy2">*</span>x<span class="br0">)</span> <span class="sy2">-</span> <a href="cpp-numeric-math-cos.html"><span class="kw1334">std::<span class="me2">cos</span></span></a><span class="br0">(</span>x<span class="br0">)</span><span class="sy2">/</span>x <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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<span class="br0">}</span></pre></div>
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</div>
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<p>输出：</p>
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<div dir="ltr" class="mw-geshi" style="text-align: left;">
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<div class="text source-text">
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<pre class="de1">j_1(1.2345) = 0.352106
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(sin x)/x^2 - (cos x)/x = 0.352106</pre></div>
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</div>
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<h3><span class="mw-headline" id=".E5.A4.96.E9.83.A8.E9.93.BE.E6.8E.A5">外部链接</span></h3>
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<p><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/SphericalBesselFunctionoftheFirstKind.html">Weisstein, Eric W. “第一类球贝塞尔函数”</a>来自 MathWorld--A Wolfram Web Resource 。</p>
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<h3><span class="mw-headline" id=".E5.8F.82.E9.98.85_2">参阅</span></h3>
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<table class="t-dsc-begin">
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-special_functions-cyl_bessel_j.html"><span class="t-lines"><span>cyl_bessel_j</span><span>cyl_bessel_jf</span><span>cyl_bessel_jl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div>
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</div>
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</td>
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<td>（第一类）圆柱贝塞尔函数<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-special_functions-sph_neumann.html"><span class="t-lines"><span>sph_neumann</span><span>sph_neumannf</span><span>sph_neumannl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div>
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</div>
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<td>球面诺依曼函数<br />
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<span class="t-mark">(函数)</span></td>
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</table>
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</div>
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<div class="visualClear"></div>
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</div>
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</div>
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