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variants of this functions
Gamma






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Gamma[z] > Integration > Definite integration > Involving the direct function





http://functions.wolfram.com/06.05.21.0006.01









  


  










Input Form





Integrate[(Gamma[a + t] Gamma[1 + a/2 + t] Gamma[b + t] Gamma[c + t] Gamma[d + t] Gamma[e + t] Gamma[f + t] Gamma[b - a - t] Gamma[-t])/ (Gamma[a/2 + t] Gamma[1 + a - c + t] Gamma[1 + a - d + t] Gamma[1 + a - e + t] Gamma[1 + a - f + t]), {t, \[Gamma] - I Infinity, \[Gamma] + I Infinity}] == Pi I ((Gamma[b] Gamma[c] Gamma[d] Gamma[e] Gamma[f] Gamma[b + c - a] Gamma[b + d - a] Gamma[b + e - a] Gamma[b + f - a])/ (Gamma[1 + a - c - e] Gamma[1 + a - d - e] Gamma[1 + a - c - d] Gamma[1 + a - c - f] Gamma[1 + a - d - f] Gamma[1 + a - e - f])) /; 2 a == b + c + d + e + f - 1 && -Min[Re[a], Re[a]/2 + 1, Re[b], Re[c], Re[d], Re[e], Re[f]] < \[Gamma] < Min[Re[b - a], 0]










Standard Form





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MathML Form







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</apply> </apply> </apply> <cn type='integer'> 0 </cn> </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