# A note on the real zeros of the incomplete gamma function

@article{Thompson2011ANO, title={A note on the real zeros of the incomplete gamma function}, author={I. Thompson}, journal={Integral Transforms and Special Functions}, year={2011}, volume={23}, pages={445 - 453} }

Asymptotic formulae that estimate the locations of real zeros of the lower incomplete gamma function are obtained using methods based in part on the original derivations by Tricomi. It is shown that these original calculations are correct, aside from some minor typographical errors, whereas later papers have overstated the accuracy of the approximations. For one of the zeros, a minor alteration to Tricomi’s working leads to a formula that is more accurate than those that have appeared in the… Expand

#### 6 Citations

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#### References

SHOWING 1-7 OF 7 REFERENCES

On the Zeros of the Incomplete Gamma Function

- Mathematics
- 1972

Some asymptotic formulae given elsewhere for the zeros of the incomplete gam- ma function -y(a, x) are corrected. A plot of a few of the zero trajectories of the function y(xw, x) is given, where x… Expand

NIST Handbook of Mathematical Functions

- Mathematics, Computer Science
- 2010

This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators and is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun. Expand

Asymptotic analysis

- Mathematics
- 1986

This paper presents an analysis of stochastic gradient-based adaptive algorithms with general cost functions. The analysis holds under mild assumptions on the inputs and the cost function. The method… Expand

Higher Transcendental Functions

- Mathematics
- Nature
- 1955

Higher Transcendental FunctionsBased, in part, on notes left by the late Prof. Harry Bateman, and compiled by the Staff of the Bateman Project. Vol. 1. Pp. xxvi + 302. 52s. Vol. 2. Pp. xvii + 396.… Expand

Fonctions hypergéométriques confluentes

- Mathematics, Physics
- 1960

© Gauthier-Villars, 1960, tous droits réservés. L’accès aux archives de la collection « Mémorial des sciences mathématiques » implique l’accord avec les conditions générales d’utilisation… Expand