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variants of this functions
Hypergeometric0F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric0F1[b,z] > Transformations > Products, sums, and powers of the direct function > Products of the direct function





http://functions.wolfram.com/07.17.16.0003.01









  


  








Input Form





Hypergeometric0F1[b, c z] Hypergeometric0F1[\[Beta], d z] == Sum[(c^m/(Pochhammer[b, m] m!)) (d^(k - m)/(Pochhammer[\[Beta], k - m] (k - m)!)) z^k, {k, 0, Infinity}, {m, 0, k}]








Standard Form





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MathML Form







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</mo> </mrow> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mi> &#946; </mi> <mo> ) </mo> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mi> m </mi> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, &quot;\[Beta]&quot;, &quot;)&quot;]], RowBox[List[&quot;k&quot;, &quot;-&quot;, &quot;m&quot;]]], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <ci> HypergeometricPFQ </ci> <list /> <list> <ci> b </ci> </list> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list /> <list> <ci> &#946; </ci> </list> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> m </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> k </ci> </uplimit> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <power /> <ci> c </ci> <ci> m </ci> </apply> <apply> <power /> <ci> d </ci> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> k </ci> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Pochhammer </ci> <ci> b </ci> <ci> m </ci> </apply> <apply> <factorial /> <ci> m </ci> </apply> <apply> <ci> Pochhammer </ci> <ci> &#946; </ci> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <apply> <factorial /> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29