TY - JOUR
T1 - On the computations of contiguous relations for 2F1 hypergeometric series
AU - Rakha, Medhat A.
AU - Ibrahim, Adel K.
AU - Rathie, Arjun K.
PY - 2009
Y1 - 2009
N2 - Contiguous relations for hypergeometric series contain an enormous amount of hidden information. Applications of contiguous relations range from the evaluation of hypergeometric series to the derivation of summation and transformation formulas for such series. In this paper, a general formula joining three Gauss functions of the form 2F1[a1, a2; a3; z] with arbitrary integer shifts is presented. Our analysis depends on using shifted operators attached to the three parameters a1, a2 and a3. We also, discussed the existence condition of our formula.
AB - Contiguous relations for hypergeometric series contain an enormous amount of hidden information. Applications of contiguous relations range from the evaluation of hypergeometric series to the derivation of summation and transformation formulas for such series. In this paper, a general formula joining three Gauss functions of the form 2F1[a1, a2; a3; z] with arbitrary integer shifts is presented. Our analysis depends on using shifted operators attached to the three parameters a1, a2 and a3. We also, discussed the existence condition of our formula.
KW - Contiguous relations
KW - Hypergeometric function
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U2 - 10.4134/CKMS.2009.24.2.291
DO - 10.4134/CKMS.2009.24.2.291
M3 - Article
AN - SCOPUS:67449152440
SN - 1225-1763
VL - 24
SP - 291
EP - 302
JO - Communications of the Korean Mathematical Society
JF - Communications of the Korean Mathematical Society
IS - 2
ER -