Contiguous relations for Meijer's G-function (Q1095287)

A number of contiguous relations for Meijer's G-function are obtained by the application of Mellin transformation. Among the relations, certain mixed (forward) recurrences as well as backward recurrences are obtained, and various other relations are developed. Some specific examples to illustrate the usefulness of the results are also mentioned in the paper. One of the author's contiguous relation (in abbreviated form) is \[ G=G[a_ 1-1]+(-1)^{q-m-n}\times [\sum^{m}_{k=1}(a_ 1-b_ k)Q(k)\times G[b_ k-1]-\sum^{q}_{k=m+1}(a_ 1-b_ k)Q(k)G[b_ k- 1]], \] where \(1\leq p<q-1\), and \[ Q(k)=\prod^{p}_{j=1}(a_ j-b_ k)/\prod^{q}_{j=1}(b_ j-b_ k). \]