<p>不知道这会有多大的帮助,但这里有几个想法太长了,不能发表评论。在</p>
<p>你需要计算<a href="https://i.stack.imgur.com/Tt5t4.gif" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Tt5t4.gif" alt="2 \cdot e^{x^2} \cdot f(\sqrt{2}x)"/></a>的积分,你<a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.special.ndtr.html#scipy.special.ndtr" rel="nofollow noreferrer">correctly identified</a>就是<a href="https://i.stack.imgur.com/qgWkq.gif" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/qgWkq.gif" alt="e^{x^2}*(1 + erf(x))"/></a>。打开括号,你可以把求和的两个部分都积分起来。在</p>
<p><a href="https://i.stack.imgur.com/EcbfJ.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/EcbfJ.png" alt="enter image description here"/></a></p>
<p>Scipy有这个<a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.special.erfi.html#scipy.special.erfi" rel="nofollow noreferrer">imaginary error function implemented</a></p>
<p>第二部分比较困难:</p>
<p><a href="https://i.stack.imgur.com/nGtc7.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/nGtc7.png" alt="enter image description here"/></a></p>
<p>这是一个<a href="https://en.wikipedia.org/wiki/Generalized_hypergeometric_function" rel="nofollow noreferrer">generalized hypergeometric function</a>。不幸的是,它看起来像scipy <a href="http://docs.scipy.org/doc/scipy/reference/special.html#hypergeometric-functions" rel="nofollow noreferrer">does not have an implementation of it</a>,但{a9}声称它确实如此。在</p>
<p>在这里我使用不带常数的不定积分,知道<code>from</code><code>to</code>值,很清楚如何使用定积分。在</p>