Mikhail Yu. Kalmykov et al JHEP02(2007)040 doi:10.1088/1126-6708/2007/02/040
Mikhail Yu. Kalmykov1,2, Bennie F.L. Ward3 and Scott Yost3
Show affiliationsIt is proved that the Laurent expansion of the following Gauss hypergeometric functions,
2F1 (I1+aε, I2+bε; I3+c ε;z) ,
2F1 (I1+aε, I2+bε; I3+½+c ε;z) ,
2F1 (I1+½+aε, I2+bε; I3+c ε;z) ,
2F1 (I1+½+aε, I2+bε; I3+½ + c ε;z) ,
2F1 (I1+½+aε, I2+½+bε; I3+½ + c ε;z) ,
where I1,I2,I3 are an arbitrary integer nonnegative numbers, a,b,c are an arbitrary numbers and ε is an arbitrary small parameters, are expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with polynomial coefficients. An efficient algorithm for the calculation of the higher-order coefficients of Laurent expansion is constructed. Some particular cases of Gauss hypergeometric functions are also discussed.
E-print Number: hep-th/0612240
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Refers: to
33Cxx Hypergeometric functions
Issue 02 (February 2007)
Received 10 January 2007, accepted for publication 24 January 2007
Published 13 February 2007
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