Fonctions hypergéométriques confluentes (1960)


Tricomi, F. G.
Mémorial des sciences mathématiques, Tome 140 (1960) 92 p URL stable : http://www.numdam.org/item?id=MSM_1960__140__1_0

Bibliographie

[1] Appell (P.) et Kampé De Fériet (J.) . _ Fonctions hypergéométriques et hypersphériques. Polynomes d'Hermite. Paris, Gauthier-Villars, 1926. JFM 52.0361.13

[2] « Bateman Projet » (Erdélyi, Magnus, Oberhettinger et Tricomi). _ Higher transcendental functions, I, II, III; Tables of integral transformations, I, II; New-York, etc., McGraw-Hill, 1953-1955.

[3] Buchholz (H.). _ Die konfluente hypergeometrische Funktion, Berlin usw, Springer, 1953. MR 54783 | Zbl 0050.07402

[4] Chang (C.), Chu (B.) et O'Brien (V.). _ An asymptotic expansion for the Whittaker function Wkm(z) . (J. Rat. Mech. and Analysis, t. 2, 1953, p. 125-135). MR 51374 | Zbl 0050.07502

[5] Erdélyi (A.), Kennedy (M.) et Mcgregor (J. L.). _ Parabolic cylinder functions of large order (J. Rat. Mech. and Analysis, t. 3, 1954, p. 461-485). MR 62875 | Zbl 0057.05502

[6] Erdélyi (A.), Kennedy (M.) et Mcgregor (J. L.). _ Asymptotic of Coulomb wave functions, I, California Inst. of Technology, Tech. Report n° 4, 1955.

[7] Erdélyi (A.) et Swanson (C. A.). _ Asymptotic forms of Coulomb wave functions, II, California Inst. of Technology, Tech. Report n° 5, 1955. MR 78407

[8] Erdélyi (A.) et Swanson (G. A.) . _ Asymptotic forms of Whittaker's confluent hypergeometric functions (Amer. Math. Soc. Mem. n° 25, 1957). Zbl 0127.29602

[9] Kummer (E. E.). _ Über die hypergeometrische, Reihe F (α, β, x) [J. reine, angew. Math. (Crelle), t. 15, 1836, p. 39-83]. Zbl 015.0528cj

[10] Mahler (K.). _ Über die Nullstellen der unvollständigen Gammafunktion (Rend. Circolo Mat. Palermo, t. 54, 1930, p. 1-41). JFM 56.0310.01

[11] Nielsen (N.). _ Theorie des Integrallogarithmus und verwandter Transzendenten, Leipzig, Teubner, 1906. JFM 37.0454.01

[12] Taylor (W. C.). _ A complete set of asymptotic formulas... [J. Math. Phys. (M. I. T.), t. 18, 1939, p. 34-49]. JFM 65.0293.02 | Zbl 0021.12304

[13] Tricomi (F. G.). _ Sulle funzioni ipergeometriche confluenti [Annali Matem. (4), t. 26, 1947-1948, p. 141-175]. MR 29451 | Zbl 0034.33704

[14] Tricomi (F. G.). _ Sugli zeri delle funzioni di cui conosce una rappresentazione asintotica (Ibid. p. 283-300). MR 30018 | Zbl 0034.32402

[15] Tricomi (F. G.). _ Sul comportamento asintotico dei polinomi di Laguerre (Ibid., t. 28, 1949, p. 263-289). MR 36355 | Zbl 0039.29903

[16] Tricomi (F. G.). _ Sulla funzione gamma incompleta (Ibid., t. 31, 1950, p. 263-279). MR 47834 | Zbl 0040.18401

[17] Tricomi (F. G.). _ A class of non orthogonal polynomials related to those of Laguerre [J. Analyse Math. (Jérusalem) , t. 1, 1957, p. 209-231]. MR 51351 | Zbl 0045.34501

[18] Tricomi (F. G.). _ Expansion of the hypergeometric function etc. (Comm. Math. Helv., t. 25, 1951, p. 196-204). MR 43949 | Zbl 0054.03302

[19] _ Zur Asymptotik der konfluenten hypergeometrischen Funktionen (Archiv der Math., t. 5, 1943, p. 376-384). MR 64209 | Zbl 0058.05806

[20] Tricomi (F. G.). _ Funzioni ipergeometriche confluenti (Monogr. Matem., C. N. R. n° 1), Roma, Cremonese, 1954. MR 76936 | Zbl 0068.28005

[21] Tricomi (F. G.). _ Konfluente hypergeometrische Funktionen (Zusammenfassender Bericht) [Z. Angew. Math. Physik (Z. A. M. P.), t. 6, 1955, p. 257-274]. MR 71583 | Zbl 0064.31001

[22] Whittaker (E. T.). et Watson (G. N.) _ A course of modern Analysis 4e éd., Cambridge, University Press, 1952. JFM 45.0433.02 | MR 1424469 | Zbl 0951.30002

B. _ TABLES NUMÉRIQUES.

[23] British. Assoc. Adv. Sc. Reports (Oxford), 1926, p. 276-294; 1927, p. 220-244.

[24] Conolly (B. W.). _ A short table of the confluent hyperg. function M (α, α, x). (Quart. J. Appl. Math., t. 2, 1950, p. 236-240). MR 36072 | Zbl 0040.35903

[25] Gran Olsson (R.). _ Tabellen der Konfluenten hyperg. Funktionen (Ingenieur-Archiv, t. 8, 1937, p. 99-103 et 373-380). JFM 63.0530.01 | Zbl 0016.31705

[26] Kuhn (T. S.) _ A convenient general solution . . . (Quart. J. Appl. Math., t. 9, 1951, p. 116). MR 48637

[27] Mac Donald (A. D.). J . Math. Phys., (M. I. T.), t. 28, 1949, p. 183-191.

[28] Middleton (D.) et Johnson (V.). _ A tabulation of selected confluent hyperg. functions, Harvard University tech. Rep. n° 140, Cambridge, Mass., 1952.

[29] Nath (P.) _ Confluent hyperg. function. (Sankhya, t. 11, 1951, p. 153-166). MR 44892 | Zbl 0044.13306

[30] Rushton (S.) et Lang (E. D.). _ Tables of the confluent hyperg. function (Ibid., t. 13, 1954, p. 377-411). MR 63492 | Zbl 0055.30202

[31] Slater (L. J.). _ On the evaluation of the confluent hyperg. function. (Proc. Cambridge Phil. Soc., t. 49, 1953, p. 612-622). MR 57014 | Zbl 0051.10103

[32] Tables of Whittaker functions (wave functions in Coulomb field). (The Tsuneta Yano Mem. Soc., Numerical Comp. Bureau, Rep. n° 9, Tokyo, 1956.) MR 81562 | Zbl 0073.34501

[33] Tables of Coulomb wave functions, National Bureau of Standard, Washington D. C., 1952. Zbl 0049.28004