I have question regarding gamma function. It is concerning ##\Gamma## function of negative integer arguments.(adsbygoogle = window.adsbygoogle || []).push({});

Is it ##\Gamma(-1)=\infty## or ##\displaystyle \lim_{x \to -1}\Gamma(x)=\infty##? So is it ##\Gamma(-1)## defined or it is ##\infty##? This question is mainly because of definition of Bessel function

[tex] J_p(x)=\sum^{\infty}_{n=0}\frac{(-1)^n}{\Gamma(n+1)\Gamma(n+p+1)}(\frac{x}{2})^{2n+p}[/tex]

For example there is relation

[tex]J_{-p}(x)=(-1)^pJ_p(x) [/tex]

What is happening with ##J_{-2}##

[tex] J_{-2}(x)=\sum^{\infty}_{n=0}\frac{(-1)^n}{\Gamma(n+1)\Gamma(n-1)}(\frac{x}{2})^{2n-2}[/tex]

for term ##n=0##?

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# A Gamma function, Bessel function

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