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variants of this functions
MeijerG






Mathematica Notation

Traditional Notation









Hypergeometric Functions > MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z] > Specific values > Specialized values > Cases with m==4 > Case {m,n,p,q}={4,1,4,4}





http://functions.wolfram.com/07.34.03.1068.01









  


  










Input Form





MeijerG[{{a}, {c, d, a - c + d}}, {{b, -1 + a - b + d, (1/2) (-1 + a + d), (a + d)/2}, {}}, z] == ((2^(a - d) Sqrt[Pi] Gamma[1 - a + b] Gamma[-b + d])/ (Gamma[1 - a + c] Gamma[1 - c + d])) z^(-1 + a) Hypergeometric2F1[1 - a + b, -b + d, 1 - a + c, (1/(2 Sqrt[z])) (Sqrt[z] - Sqrt[1 + z])] Hypergeometric2F1[1 - a + b, -b + d, 1 - c + d, (1/(2 Sqrt[z])) (Sqrt[z] - Sqrt[1 + z])] /; !IntervalMemberQ[Interval[{-Infinity, 0}], z]










Standard Form





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MathML Form







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&quot;, SqrtBox[&quot;z&quot;]]]], Hypergeometric2F1, Rule[Editable, True]], Hypergeometric2F1, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] </annotation> </semantics> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29