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AppellF1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > AppellF1[a,b1,b2,c,z1,z2] > Series representations > Generalized power series > Expansions at z1==infinity > For the function itself





http://functions.wolfram.com/07.36.06.0015.02









  


  








Input Form





AppellF1[a, Subscript[b, 1], Subscript[b, 2], c, Subscript[z, 1], Subscript[z, 2]] == (((Gamma[c] Gamma[Subscript[b, 1] - a])/(Gamma[c - a] Gamma[Subscript[b, 1]])) AppellF1[a, 1 + a - c, Subscript[b, 2], 1 + a - Subscript[b, 1], 1/Subscript[z, 1], Subscript[z, 2]/ Subscript[z, 1]])/(-Subscript[z, 1])^a + ((Gamma[c]/Gamma[a]) Sum[((Gamma[a - Subscript[b, 1] + k] Pochhammer[Subscript[b, 2], k])/(k! Gamma[c - Subscript[b, 1] + k])) Hypergeometric2F1[Subscript[b, 1], 1 - c + Subscript[b, 1] - k, 1 - a + Subscript[b, 1] - k, 1/Subscript[z, 1]] Subscript[z, 2]^k, {k, 0, Infinity}])/(-Subscript[z, 1])^Subscript[b, 1] /; !Element[a - Subscript[b, 1], Integers]








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