Fonctions hypergéométriques confluentes

F. G. Tricomi

  • Publisher: Gauthier-Villars, 1960

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Tricomi, F. G.. Fonctions hypergéométriques confluentes. 1960. <http://eudml.org/doc/192660>.

@book{Tricomi1960,
author = {Tricomi, F. G.},
keywords = {special functions},
language = {fre},
publisher = {Gauthier-Villars},
title = {Fonctions hypergéométriques confluentes},
url = {http://eudml.org/doc/192660},
year = {1960},
}

TY - BOOK
AU - Tricomi, F. G.
TI - Fonctions hypergéométriques confluentes
PY - 1960
PB - Gauthier-Villars
LA - fre
KW - special functions
UR - http://eudml.org/doc/192660
ER -

References

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  1. [1] APPELL ( P.) et KAMPÉ DE FÉRIET ( J.) . _ Fonctions hypergéométriques et hypersphériques. Polynomes d'Hermite. Paris, Gauthier-Villars, 1926. Zbl52.0361.13JFM52.0361.13
  2. [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. [3] BUCHHOLZ ( H.). _ Die konfluente hypergeometrische Funktion, Berlin usw, Springer, 1953. Zbl0050.07402MR54783
  4. [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). Zbl0050.07502MR51374
  5. [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). Zbl0057.05502MR62875
  6. [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. [7] ERDÉLYI ( A.) et SWANSON ( C. A.). _ Asymptotic forms of Coulomb wave functions, II, California Inst. of Technology, Tech. Report n° 5, 1955. MR78407
  8. [8] ERDÉLYI ( A.) et SWANSON ( G. A.) . _ Asymptotic forms of Whittaker's confluent hypergeometric functions (Amer. Math. Soc. Mem. n° 25, 1957). Zbl0127.29602
  9. [9] KUMMER ( E. E.). _ Über die hypergeometrische, Reihe F (α, β, x) [J. reine, angew. Math. (Crelle), t. 15, 1836, p. 39-83]. 
  10. [10] MAHLER ( K.). _ Über die Nullstellen der unvollständigen Gammafunktion (Rend. Circolo Mat. Palermo, t. 54, 1930, p. 1-41). Zbl56.0310.01JFM56.0310.01
  11. [11] NIELSEN ( N.). _ Theorie des Integrallogarithmus und verwandter Transzendenten, Leipzig, Teubner, 1906. Zbl37.0454.01JFM37.0454.01
  12. [12] TAYLOR ( W. C.). _ A complete set of asymptotic formulas... [J. Math. Phys. (M. I. T.), t. 18, 1939, p. 34-49]. Zbl0021.12304JFM65.0293.02
  13. [13] TRICOMI ( F. G.). _ Sulle funzioni ipergeometriche confluenti [Annali Matem. (4), t. 26, 1947-1948, p. 141-175]. Zbl0034.33704MR29451
  14. [14] TRICOMI ( F. G.). _ Sugli zeri delle funzioni di cui conosce una rappresentazione asintotica (Ibid. p. 283-300). Zbl0034.32402MR30018
  15. [15] TRICOMI ( F. G.). _ Sul comportamento asintotico dei polinomi di Laguerre (Ibid., t. 28, 1949, p. 263-289). Zbl0039.29903MR36355
  16. [16] TRICOMI ( F. G.). _ Sulla funzione gamma incompleta (Ibid., t. 31, 1950, p. 263-279). Zbl0040.18401MR47834
  17. [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]. Zbl0045.34501MR51351
  18. [18] TRICOMI ( F. G.). _ Expansion of the hypergeometric function etc. (Comm. Math. Helv., t. 25, 1951, p. 196-204). Zbl0054.03302MR43949
  19. [19] _ Zur Asymptotik der konfluenten hypergeometrischen Funktionen (Archiv der Math., t. 5, 1943, p. 376-384). Zbl0058.05806MR64209
  20. [20] TRICOMI ( F. G.). _ Funzioni ipergeometriche confluenti (Monogr. Matem., C. N. R. n° 1), Roma, Cremonese, 1954. Zbl0068.28005MR76936
  21. [21] TRICOMI ( F. G.). _ Konfluente hypergeometrische Funktionen (Zusammenfassender Bericht) [Z. Angew. Math. Physik (Z. A. M. P.), t. 6, 1955, p. 257-274]. Zbl0064.31001MR71583
  22. [22] WHITTAKER ( E. T.). et WATSON ( G. N.) _ A course of modern Analysis 4e éd., Cambridge, University Press, 1952. Zbl0951.30002MR1424469JFM45.0433.02
  23. B. _ TABLES NUMÉRIQUES. 
  24. [23] British. Assoc. Adv. Sc. Reports (Oxford), 1926, p. 276-294; 1927, p. 220-244. 
  25. [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). Zbl0040.35903MR36072
  26. [25] GRAN OLSSON ( R.). _ Tabellen der Konfluenten hyperg. Funktionen (Ingenieur-Archiv, t. 8, 1937, p. 99-103 et 373-380). Zbl0016.31705JFM63.0530.01
  27. [26] KUHN ( T. S.) _ A convenient general solution . . . (Quart. J. Appl. Math., t. 9, 1951, p. 116). MR48637
  28. [27] MAC DONALD ( A. D.). J . Math. Phys., (M. I. T.), t. 28, 1949, p. 183-191. 
  29. [28] MIDDLETON ( D.) et JOHNSON ( V.). _ A tabulation of selected confluent hyperg. functions, Harvard University tech. Rep. n° 140, Cambridge, Mass., 1952. 
  30. [29] NATH ( P.) _ Confluent hyperg. function. (Sankhya, t. 11, 1951, p. 153-166). Zbl0044.13306MR44892
  31. [30] RUSHTON ( S.) et LANG ( E. D.). _ Tables of the confluent hyperg. function (Ibid., t. 13, 1954, p. 377-411). Zbl0055.30202MR63492
  32. [31] SLATER ( L. J.). _ On the evaluation of the confluent hyperg. function. (Proc. Cambridge Phil. Soc., t. 49, 1953, p. 612-622). Zbl0051.10103MR57014
  33. [32] Tables of Whittaker functions (wave functions in Coulomb field). (The Tsuneta Yano Mem. Soc., Numerical Comp. Bureau, Rep. n° 9, Tokyo, 1956.) Zbl0073.34501MR81562
  34. [33] Tables of Coulomb wave functions, National Bureau of Standard, Washington D. C., 1952. Zbl0049.28004

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