Turkish Journal of Mathematics
On a new identity for the H-function with applications to the summation of hypergeometric series
Using generalized hypergeometric functions to perform symbolic manipulations of equations is of great importance to pure and applied scientists. There are in the literature a great number of identities for the Meijer-G function. On the other hand, when more complex expressions arise, that function is not capable of representing them. The H-function is an alternative to overcome this issue, as it is a generalization of the Meijer-G function. In the present paper, a new identity for the H-function is derived. In short, this result enables one to split a particular H-function into the sum of two other H-functions. The new relation in addition to an old result are applied to the summation of hypergeometric series. Finally, some relations between H-functions and elementary functions are built.
H-function, hypergeometric sum, identity
RATHIE, ARJUN KUMAR; OZELIM, LUAN CARLOS DE SENA MONTEIRO; and RATHIE, PUSHPA NARAYAN
"On a new identity for the H-function with applications to the summation of hypergeometric series,"
Turkish Journal of Mathematics: Vol. 42:
3, Article 16.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/16