[123.8.1] The H-function of order m,n,p,q∈N4 and with parameters
Ai∈R+(i=1,…,p), Bi∈R+(i=1,…,q),
ai∈C(i=1,…,p), and bi∈C(i=1,…,q)
is defined for z∈C,z≠0 by the contour integral
[5, 32]
| Hp,qm,n(z|a1,A1,…,ap,Apb1,B1,…,bq,Bq)=12πi∫Lη(s)z-sds | | (14) |
where the integrand is
| ηs=∏i=1mΓbi+Bis∏i=1nΓ1-ai-Ais∏i=n+1pΓai+Ais∏i=m+1qΓ1-bi-Bis. | | (15) |
[123.8.2] In (14) z-s=exp-slogz-iargz and argz
is not necessarily the principal value.
[123.8.3] The integers m,n,p,q must satisfy
and empty products are interpreted as being unity.
[123.8.4] For the conditions on the other parameters
and the path L of integration the reader is referred
to the literature [5] (see [13, p.120ff]
for a brief summary).
