<commit_before><!DOCTYPE html>
<html>
<head>
<title>spherical_bessel_J &mdash; SageMath</title>
<link rel="stylesheet" type="text/css" href="../style.css">
</head>

<body>

<script src="https://sagecell.sagemath.org/static/jquery.min.js"></script>
<script src="https://sagecell.sagemath.org/static/embedded_sagecell.js"></script>
<script src="../setup.js"></script>

<p class="sagemath"> spherical_bessel_J( <i>n</i>, <i>z</i> ) </p>

<p>The spherical Bessel function of the first kind of <i>z</i> in SageMath. Defined by</p>

\[ j_n(z) = \sqrt{ \frac{ \pi }{ 2z } } j_{n+\frac{1}{2}}(z) \]

<p>Plot on the real axis:</p>

<div class="sagemathcell">
<script type="text/x-sage">

@interact
def fun( n=slider(0,10,step_size=1) ):

  show( plot( spherical_bessel_J(n,x), x, 0, 20, figsize=[4,2], rgbcolor=(0,.5,1) ) )

</script>
</div>

<p>Series expansion about the origin:</p>

<div class="sagemathcell">
<script type="text/x-sage">

@interact
def fun( n=slider(0,10,step_size=1) ):

  var('z')
  show( maxima( spherical_bessel_J(n,z) ).taylor(z,0,n+7) )

</script><commit_msg>Fix definition<commit_after><!DOCTYPE html>
<html>
<head>
<title>spherical_bessel_J &mdash; SageMath</title>
<link rel="stylesheet" type="text/css" href="../style.css">
</head>

<body>

<script src="https://sagecell.sagemath.org/static/jquery.min.js"></script>
<script src="https://sagecell.sagemath.org/static/embedded_sagecell.js"></script>
<script src="../setup.js"></script>

<p class="sagemath"> spherical_bessel_J( <i>n</i>, <i>z</i> ) </p>

<p>The spherical Bessel function of the first kind of <i>z</i> in SageMath. Defined by</p>

\[ j_n(z) = \sqrt{ \frac{ \pi }{ 2z } } J_{n+\frac{1}{2}}(z) \]

<p>Plot on the real axis:</p>

<div class="sagemathcell">
<script type="text/x-sage">

@interact
def fun( n=slider(0,10,step_size=1) ):

  show( plot( spherical_bessel_J(n,x), x, 0, 20, figsize=[4,2], rgbcolor=(0,.5,1) ) )

</script>
</div>

<p>Series expansion about the origin:</p>

<div class="sagemathcell">
<script type="text/x-sage">

@interact
def fun( n=slider(0,10,step_size=1) ):

  var('z')
  show( maxima( spherical_bessel_J(n,z) ).taylor(z,0,n+7) )

</script>
{'fraction_non_alphanumeric': 0.2275894101254064, 'fraction_numerical': 0.019507663725034836, 'mean_word_length': 5.261627906976744, 'pattern_counts': {'":': 0, '<': 73, '<?xml version=': 0, '>': 73, 'https://': 4, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'dir': 'git-commits-cleaned', 'id': '2955662', 'n_tokens_mistral': 955, 'n_tokens_neox': 906, 'n_words': 174}