Approximating real Pochhammer products: a comparison with powers

Vito Lampret

Open Mathematics (2009)

  • Volume: 7, Issue: 3, page 493-505
  • ISSN: 2391-5455

Abstract

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Accurate estimates of real Pochhammer products, lower (falling) and upper (rising), are presented. Double inequalities comparing the Pochhammer products with powers are given. Several examples showing how to use the established approximations are stated.

How to cite

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Vito Lampret. "Approximating real Pochhammer products: a comparison with powers." Open Mathematics 7.3 (2009): 493-505. <http://eudml.org/doc/269436>.

@article{VitoLampret2009,
abstract = {Accurate estimates of real Pochhammer products, lower (falling) and upper (rising), are presented. Double inequalities comparing the Pochhammer products with powers are given. Several examples showing how to use the established approximations are stated.},
author = {Vito Lampret},
journal = {Open Mathematics},
keywords = {Approximation; Double inequality; Falling factorial; Lower factorial; Pochhammer product; Rising factorial; Sequential product; Upper factorial; approximation; double inequality; falling factorial; lower factorial; rising factorial; sequential product; upper factorial},
language = {eng},
number = {3},
pages = {493-505},
title = {Approximating real Pochhammer products: a comparison with powers},
url = {http://eudml.org/doc/269436},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Vito Lampret
TI - Approximating real Pochhammer products: a comparison with powers
JO - Open Mathematics
PY - 2009
VL - 7
IS - 3
SP - 493
EP - 505
AB - Accurate estimates of real Pochhammer products, lower (falling) and upper (rising), are presented. Double inequalities comparing the Pochhammer products with powers are given. Several examples showing how to use the established approximations are stated.
LA - eng
KW - Approximation; Double inequality; Falling factorial; Lower factorial; Pochhammer product; Rising factorial; Sequential product; Upper factorial; approximation; double inequality; falling factorial; lower factorial; rising factorial; sequential product; upper factorial
UR - http://eudml.org/doc/269436
ER -

References

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  2. [2] Atkinson K.E., An introduction to numerical analysis, J. Wiley & Sons, N.Y., 1989 Zbl0718.65001
  3. [3] Davis P.J., Rabinowitz P., Methods of numerical integration, Academic Press, Chestnut Hill, MA., 1984 Zbl0537.65020
  4. [4] Díaz R., Pariguan E., On hypergeometric functions and Pochhammer k-symbol, Divulg. Mat., 2007, 15, 179–192 Zbl1163.33300
  5. [5] Graham R.L., Knuth D.E., Patashnik O., Concrete mathematics, Addison-Wesley, Reading, MA, 1994 Zbl0836.00001
  6. [6] Kahn P.B., Mathematical methods for scientists and engineers, John Wiley & Sons, N.Y., 1990. Zbl0925.00008
  7. [7] Knopp K., Theory and applications of infinite series, Hafner, N.Y., 1971 
  8. [8] Lampret V., The Euler-Maclaurin and Taylor formulas: Twin, elementary derivations, Math. Mag., 2001, 74, 109–122 Zbl1018.41020
  9. [9] Lampret V., An invitation to Hermite’s integration and summation: A Comparison between Hermite’s and Simpson’s rules, SIAM Rev., 2004, 46, 311–328 http://dx.doi.org/10.1137/S0036144502416308 Zbl1065.41051
  10. [10] Spivey M.Z., The Euler-Maclaurin formula and sums of powers, Math. Mag., 2006, 79, 61–65 http://dx.doi.org/10.2307/27642905 Zbl1151.11308
  11. [11] Wolfram S., Mathematica, Version 6.0, Wolfram Research, Inc., 1988–2008 

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