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AppellF1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > AppellF1[a,b1,b2,c,z1,z2] > General characteristics > Branch cuts > With respect to z1





http://functions.wolfram.com/07.36.04.0021.01









  


  








Input Form





Limit[AppellF1[a, Subscript[b, 1], Subscript[b, 2], c, Subscript[x, 1] + I \[Epsilon], Subscript[z, 2]], \[Epsilon] -> Plus[0]] == E^(2 I Pi (a - c + Subscript[b, 1])) AppellF1[a, Subscript[b, 1], Subscript[b, 2], c, Subscript[x, 1], Subscript[z, 2]] + ((2 I E^(I Pi (a - c + Subscript[b, 1])) Pi Gamma[c])/ (Gamma[c - a] Gamma[1 + a - c + Subscript[b, 1]] Gamma[c - Subscript[b, 1]])) HypergeometricPFQ[ {{a}, {Subscript[b, 1]}, {Subscript[b, 2]}}, {{}, {1 + a - c + Subscript[b, 1]}, {c - Subscript[b, 1]}}, 1 - Subscript[x, 1], Subscript[z, 2]] /; Subscript[x, 1] > 1








Standard Form





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MathML Form







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Rule Form





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





2001-10-29