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Next: <a href="maxima_85.html#Bessel-Functions" accesskey="n" rel="next">Bessel Functions</a>, Up: <a href="maxima_83.html#Special-Functions" accesskey="u" rel="up">Special Functions</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Introduction-to-Special-Functions-1"></a>
<h3 class="section">15.1 Introduction to Special Functions</h3>
<p>Special function notation follows:
</p>
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<pre class="example">bessel_j (index, expr) Bessel function, 1st kind
bessel_y (index, expr) Bessel function, 2nd kind
bessel_i (index, expr) Modified Bessel function, 1st kind
bessel_k (index, expr) Modified Bessel function, 2nd kind
hankel_1 (v,z) Hankel function of the 1st kind
hankel_2 (v,z) Hankel function of the 2nd kind
struve_h (v,z) Struve H function
struve_l (v,z) Struve L function
assoc_legendre_p[v,u] (z) Legendre function of degree v and order u
assoc_legendre_q[v,u] (z) Legendre function, 2nd kind
%f[p,q] ([], [], expr) Generalized Hypergeometric function
gamma (z) Gamma function
gamma_incomplete_lower (a,z) Lower incomplete gamma function
gamma_incomplete (a,z) Tail of incomplete gamma function
hypergeometric (l1, l2, z) Hypergeometric function
%s[u,v] (z) Lommel "small" s function
slommel[u,v] (z) Lommel "big" S function
%m[u,k] (z) Whittaker function, 1st kind
%w[u,k] (z) Whittaker function, 2nd kind
erfc (z) Complement of the erf function
expintegral_e (v,z) Exponential integral E
expintegral_e1 (z) Exponential integral E1
expintegral_ei (z) Exponential integral Ei
expintegral_li (z) Logarithmic integral Li
expintegral_si (z) Exponential integral Si
expintegral_ci (z) Exponential integral Ci
expintegral_shi (z) Exponential integral Shi
expintegral_chi (z) Exponential integral Chi
kelliptic (z) Complete elliptic integral of the first
kind (K)
parabolic_cylinder_d (v,z) Parabolic cylinder D function
</pre></div>
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Categories:<a href="maxima_424.html#Category_003a-Bessel-functions">Bessel functions</a>
·<a href="maxima_424.html#Category_003a-Airy-functions">Airy functions</a>
·<a href="maxima_424.html#Category_003a-Special-functions">Special functions</a>
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Next: <a href="maxima_85.html#Bessel-Functions" accesskey="n" rel="next">Bessel Functions</a>, Up: <a href="maxima_83.html#Special-Functions" accesskey="u" rel="up">Special Functions</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
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