On the zeros of the incomplete gamma function
HTML articles powered by AMS MathViewer
- by K. S. Kölbig PDF
- Math. Comp. 26 (1972), 751-755 Request permission
Abstract:
Some asymptotic formulae given elsewhere for the zeros of the incomplete gamma function $\gamma (a,x)$ are corrected. A plot of a few of the zero trajectories of the function $\gamma (xw,x)$ is given, where $x$ is a real parameter. Based on theoretical work by Mahler, it is seen that the zero trajectories of $\gamma (xw,x)$ lie in a finite region of the complex $w$-plane.References
- Milton Abramowitz and Irene A. Stegun (eds.), Handbook of mathematical functions, with formulas, graphs and mathematical tables, National Bureau of Standards Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D.C., 20402, 1966. Fifth printing, with corrections; National Bureau of Standards, Washington, D.C., (for sale by the Superintendent of Documents). MR 0208798
- Philip Franklin, Calculation of the complex zeros of the function $P(z)$ complementary to the incomplete gamma function, Ann. of Math. (2) 21 (1919), no. 1, 61–63. MR 1503528, DOI 10.2307/2007135
- Alwin Walther, Über die reellen Nullstellen der unvollständigen Gammafunktion $P(z)$, Math. Z. 23 (1925), no. 1, 238–245 (German). MR 1544740, DOI 10.1007/BF01506230
- G. Rasch, Über die Nullstellen der unvollständigen Gammafunktion $P(z,\varrho )$, Math. Z. 29 (1929), no. 1, 300–318 (German). MR 1545006, DOI 10.1007/BF01180532
- Einar Hille and G. Rasch, Über die Nullstellen der unvollständigen Gammafunktion $P(z,\varrho )$, Math. Z. 29 (1929), no. 1, 319–334 (German). MR 1545007, DOI 10.1007/BF01180533 K. Mahler, “Ueber die Nullstellen der unvollstaendigen Gammafunktion,” Rend. Circ. Mat. Palermo, v. 46, 1930, pp. 1-42.
- F. G. Tricomi, Asymptotische Eigenschaften der unvollständigen Gammafunktion, Math. Z. 53 (1950), 136–148 (German). MR 45253, DOI 10.1007/BF01162409
- Francesco G. Tricomi, Funzioni ipergeometriche confluenti, Edizioni Cremonese, Roma, 1954 (Italian). MR 0076936
- F. G. Tricomi, Fonctions hypergéométriques confluentes, Mémor. Sci. Math., Fasc. CXL, Gauthier-Villars, Paris, 1960 (French). MR 0120409
- K. S. Kölbig, Complex zeros of an incomplete Riemann zeta function and of the incomplete gamma function, Math. Comp. 24 (1970), 679–696. MR 273787, DOI 10.1090/S0025-5718-1970-0273787-8
- K. S. Kölbig, Complex zeros of two incomplete Riemann zeta functions, Math. Comp. 26 (1972), 551–565. MR 303686, DOI 10.1090/S0025-5718-1972-0303686-6 A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Higher Transcendental Functions. Vol. II, McGraw-Hill, New York, 1953. MR 15, 419.
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Math. Comp. 26 (1972), 751-755
- MSC: Primary 65D20
- DOI: https://doi.org/10.1090/S0025-5718-1972-0326994-1
- MathSciNet review: 0326994