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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==1 > For the function itself





http://functions.wolfram.com/07.36.06.0009.01









  


  










Input Form





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










Standard Form





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MathML Form







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</apply> </apply> </apply> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <times /> <apply> <ci> Pochhammer </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <ci> k </ci> </apply> <apply> <power /> <apply> <factorial /> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <plus /> <ci> c </ci> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> 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Rule Form





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





2001-10-29





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