Difference between revisions of "Bessel-Clifford"

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Let $\pi(x)=\dfrac{1}{\Gamma(x+1)}$, where $\Gamma$ denotes the [[gamma function]]. The Bessel-Clifford function $\mathcal{C}_n$ is defined by
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The Bessel-Clifford function $\mathcal{C}_n$ is defined by
$$\mathcal{C}_n(z)=\displaystyle\sum_{k=0}^{\infty} \pi(k+n)\dfrac{z^k}{k!}.$$
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$$\mathcal{C}_n(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{1}{\Gamma(k+n+1)} \dfrac{z^k}{k!},$$
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where $\dfrac{1}{\Gamma}$ denotes the [[reciprocal gamma]] function.
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<div align="center">
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<gallery>
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File:Besselcliffordn=0plot.png|Graph of $\mathcal{C}_0$ on $[-5,15]$.
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</gallery>
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</div>
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=Properties=
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[[Derivative of Bessel-Clifford]]<br />
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[[Bessel J in terms of Bessel-Clifford]]<br />
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[[Relationship between Bessel-Clifford and hypergeometric 0F1]]<br />
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=References=
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Latest revision as of 16:03, 29 April 2017

The Bessel-Clifford function $\mathcal{C}_n$ is defined by $$\mathcal{C}_n(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{1}{\Gamma(k+n+1)} \dfrac{z^k}{k!},$$ where $\dfrac{1}{\Gamma}$ denotes the reciprocal gamma function.


Properties

Derivative of Bessel-Clifford
Bessel J in terms of Bessel-Clifford
Relationship between Bessel-Clifford and hypergeometric 0F1

References