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Asymptotic expansions and inequalities for hypergeometric function

  • S. Ponnusamy (a1) and M. Vuorinen (a2)
  • DOI:
  • Published online: 01 February 2010

Ramanujan's work on the asymptotic behaviour of the hypergeometric function has been recently refined to the zero-balanced Gaussian hypergeometric function F(a, b; a + b; x) as x→1.We extend these results for F(a, b; c; x) when a, b, c>0 and c<a + b.

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A1.H. Alzer . Some gamma function inequalities. Math. Comput., 60 (1993), 337346.

ABRVV.G. D. Anderson R. W. Barnard K. C. Richards M. K. Vamanamurthy and M. Vuorinen . Inequalities for zero-balanced hypergeometric functions. Trans. Amer. Math. Soc., 347 (1995), 17131723.

B.B. C. Berndt . Ramanujan's Notebooks, Part II (Springer, Berlin, 1989).

BI.J. Bustoz and M. E. H. Ismail . On gamma function inequalities. Math. Comput., 47 (1986), 659667.

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