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