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Matrix solutions of the functional equation of the gamma function

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References

  1. Anastassiadis, J,Une propriete de la fonction gamma Bull Sci Math (2)81 (1957), 116–118

    Google Scholar 

  2. Artin, E,The gamma function Holt, Rinehard and Winston, 1964 English translation by M Butler of “Einfuhrung in die Theorie der Gammafunktion”, Hamb Math Einzelschr 11, Verlag B G Teuber, 1931

  3. Bellman, R,Introduction to matrix analysis 2nd Ed, McGraw-Hill, 1970

  4. Bohr, H andMollerup, J,Loerebog i matematisk analyse III Graenseprocessor Købenavn, 1922, pp 149–164

  5. Buchheim, A,An extension of a theorem of Professor Sylvester relating to matrices Philos Mag (5),22 (1886), 173–174

    Google Scholar 

  6. Carlson, B C,Special functions of applied mathematics Acad Press, 1977

  7. Cipolla, M,Sulle matrice expressions analitiche di un altra Rend Circ Mat Palermo56 (1932), 144–154

    Google Scholar 

  8. Coddington, E A andLevinson, N,Theory of ordinary differential equations McGraw-Hill, 1955

  9. Copson, E T,An introduction to the theory of functions of a complex variable Oxford, 1960

  10. Courant, R andJohn, F,Introduction to calculus and analysis, Vol 2 J Wiley & Sons, 1974

  11. Curtis, C W,Linear algebra Allyn & Bacon, 1965

  12. Dunford, N andSchwartz, J T,Linear operators part I General Theory, Interscience, 1966

  13. Evard, J C,On matrix functions which commute with their derivative Linear Algebra Appl68 (1985), 145–178

    Google Scholar 

  14. Fantappe, L,Le calcul des matrices C R Acad Sci Paris186 (198), 619–621

    Google Scholar 

  15. Finkbeiner, D T,Introduction of matrices and linear transformations Freeman, 1960

  16. Frobenius, G,Uber die cogredienten Transformationen der biblinearen Formen Sitzungsber Preuss Akad Wiss Berlin, 1986, pp 7 16

  17. Giorgi, G,Nuove osservazioni sulle funzioni delle matrici Atti Acad Naz Lincei Rend Cl Sci Fis Mat Natur (6)8 (1928), 3–8

    Google Scholar 

  18. Goldberg, J L andSchwartz, A J,Systems of ordinary differential equations an introduction Harper & Row, 1972

  19. Hensel, K,Über Potenzreihen von Matrizen J Reine Angew Math 155 (1926), 107–110

    Google Scholar 

  20. Hoffman, K andKunze, R,Linear algebra 2nd Ed, Prentice Hall, 1971

  21. Jacobsen, N,Lectures in abstract algebra, II, Linear Algebra Springer-Verlag, 1975

  22. Kairies, Hans-Heinrich,Zur axiomatischen Charakterisierung der Gammafunktion J Reine Agnew Math236 (1969), 103–111

    Google Scholar 

  23. Kairies, Hans-Heinrich,Convexity in the theory of the gamma function General inequalities, I (Proc First Internat Conf Math Res Inst, Oberwolfach, 1976), pp 49–62, Birkhauser, Basel, 1978

    Google Scholar 

  24. Kuczma, M,Functional equations in a single variable PWN-Polish Sci Pub, 1968

  25. Laguerre, E N,Sur le calcul des systemes lineares, 1867 Reprinted in Oeuvres, t 1, 1898, 221 267

  26. Lebedev, N N,Special functions and their applications Prentice-Hall Inc, 1965

  27. Lucht, L,Zur Charakterisierung der Gamma Funktion J Reine Agnew Math288 (1976), 77–85

    Google Scholar 

  28. MacDuffee, C C,The theory of matrices Chelsea, 1946

  29. Mal'cev, A I,Foundations of linear algebra (English translation) Freeman, 1963

  30. Marcus, M andMinc, H,A survey of matrix theory and matrix inequalities Allyn Bacon, 1964

  31. Muldoon, M E,Some monotonicity properties and characterizations of the gamma function Aequationes Math18 (1978), 54–63

    Google Scholar 

  32. Mutafian, C,Les applications lineaires Vuibert, 1979

  33. Noble, B andDaniel, J W,Applied linear algebra, 2nd Ed Prentice-Hall, 1977

  34. Pease, M C,Methods of matrix algebra Academic Press, 1965

  35. Poincaré, H,Sur les groupes continus Proc Cambridge Philos Soc 18, 1899, 220–255 Reprinted in Oeuvres 3, 173–212

    Google Scholar 

  36. Pullman, N J,Matrix theory and its applications Dekker, 1976

  37. Richter, H,Über Matrixfunktionen Math Ann122 (1950), 16–34

    Google Scholar 

  38. Rinehart, R F,The equivalence of definitions of a matrix function Amer Math Monthly62 (1955), 395–414

    Google Scholar 

  39. Saaty, T,Modern nonlinear equations McGraw-Hill, 1967

  40. Schwerdtfeger, H,Les Fonctiones des Matrices I, Les Fonctiones Univalentes Actualites Sci Indust No 649, Paris, Herman, 1938

    Google Scholar 

  41. Spain, B andSmith, M G,Functions of mathematical physics Van Nostrand Reinhold, 1970

  42. Strang, G,Linear algebra and its applications, 2nd Ed Academic Press, 1980

  43. Sylvester, J J,On the equation to the secular inequalities in the planetary theory Philos-Mag16 (1883), 267–269 Reprinted in Collected Papers4, 110–111

    Google Scholar 

  44. Sylvester, J J,Sur les puissances et les racines de substitutions linearies C R Acad Sci Paris94 (1882), 55–59 Reprinted in Collected Papers 3, 562 564

    Google Scholar 

  45. Weyr, E,Note sur la theorie de quantites complexes formées avec n unites principales Bull Sci Math (2)11 (1887), 205–215

    Google Scholar 

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Heuvers, K.J., Moak, D. Matrix solutions of the functional equation of the gamma function. Aeq. Math. 33, 1–17 (1987). https://doi.org/10.1007/BF01836147

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AMS (1980) subject classification

  • Primary 39A35, 33A15, 39A05