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Some expansions of hypergeometric functions in series of hypergeometric functions†

Published online by Cambridge University Press:  18 May 2009

H. M. Srivastava  and
Rekha Panda
H. M. Srivastava
Affiliation:
Department of MathematicsUniversity of VictoriaVictoria, British Columbia, CanadaV8W 2Y2
Rekha Panda
Affiliation:
Department of MathematicsUniversity of VictoriaVictoria, British Columbia, CanadaV8W 2Y2
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Throughout the present note we abbreviate the set of p parameters a1,…,ap by (ap), with similar interpretations for (bq), etc. Also, by [(ap)]m we mean the product , where [λ]m = Г(λ + m)/ Г(λ), and so on. One of the main results we give here is the expansion formula

(1)

which is valid, by analytic continuation, when, p,q,r,s,t and u are nonnegative integers such that p+r < q+s+l (or p+r = q+s+l and |zω| <1), p+t < q+u (or p + t = q + u and |z| < 1), and the various parameters including μ are so restricted that each side of equation (1) has a meaning.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 17 , Issue 1 , January 1976 , pp. 17 - 21
Copyright
Copyright © Glasgow Mathematical Journal Trust 1976

References

REFERENCES

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