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The linear differential equation whose solutions are the products of solutions of two given differential equations. (English) Zbl 0476.34008

34M99Differential equations in the complex domain
34A30Linear ODE and systems, general
15A03Vector spaces, linear dependence, rank
Full Text: DOI
[1] Appell, P.: Sur la transformation des équations différentielles linéaires. C. R. Acad. sci. Paris 91, 211-214 (1880)
[2] Bellman, R.: On the linear differential equation whose solutions are the products of solutions of two given linear differential equations. Boll. un. Mat. ital. 12, 12-15 (1957) · Zbl 0077.29101
[3] Bellman, R.: Introduction to matrix analysis. (1970) · Zbl 0216.06101
[4] Clausen, T.: Beitrag zur theorie der reihen. 3, 92-95 (1828) · Zbl 003.0099cj
[5] Coddington, E. A.; Levinson, N.: Theory of ordinary differential equations. (1955) · Zbl 0064.33002
[6] Cohn, P. M.: Algebra. (1977) · Zbl 0341.00002
[7] Connell, I.: An estimate for the dimension of the product of two vector spaces. Linear and multilinear algebra 4, 273-275 (1977) · Zbl 0351.15002
[8] Curtiss, D. R.: The vanishing of the Wronskian and the problem of linear dependence. Math. ann. 65, 282-298 (1908) · Zbl 39.0354.02
[9] Hobson, E. W.: The theory of spherical and ellipsoidal harmonics. (1931) · Zbl 0004.21001
[10] Hurewicz, W.: Lectures on ordinary differential equations. (1958) · Zbl 0082.29702
[11] Lang, S.: Algebra. (1965) · Zbl 0193.34701
[12] Marcus, M.; Minc, H.: A survey of matrix theory and matrix inequalities. (1964) · Zbl 0126.02404
[13] Neuman, F. E.: Beiträge zur theorie der kugelfunktionen. (1878)
[14] Nicholson, J. W.: The products of Bessel functions. Quart. J. 43, 78-100 (1912) · Zbl 42.0489.01
[15] Nielsen, N.: Handbuch der theorie der cylinderfunktionen. (1904) · Zbl 35.0476.03
[16] Nielsen, N.: Théories des fonctions métasphériques. (1911)
[17] Orr, W. Mcf: Theorems relating to the product of two hypergeometric series. Trans. Cambridge philos. Soc. 17, 1-15 (1899)
[18] Palamà, G.: Sulle equazioni differenziali lineari soddisfatte dal prodotto di integrali particolari di due equazioni differenziali lineari omogenee assegnate e su alcune formule integrali dei polinomi di Laguerre e di Hermite. Ann. mat. Pura appl. 18, 309-325 (1939) · Zbl 65.0282.01
[19] Richard, U.: Sviluppo in serie delle funzioni ker2vx + kei2vx. Atti accad. Sci. Torino cl. Sci. fis. Mat. natur. 91, 1-20 (1956--1957)
[20] Sandham, H. F.: A square and a product of hupergeometric functions. Quart. J. Math. Oxford ser. 7, 153-154 (1956) · Zbl 0071.06303
[21] Šapkarev, I. A.: Uber lineare differentialgleichungen mit der eigenschaft $da{\beta}$ k-te potenzen der integrale einer linearen differentialgleichung zweiter ordnung ihre integrale sind. Mat. vesnik 19, 67-70 (1967) · Zbl 0283.34016
[22] Slater, L. J.: Confluent hypergeometric functions. (1960) · Zbl 0086.27502
[23] Watson, G. N.: A treatise on the theory of Bessel functions. (1944) · Zbl 0063.08184
[24] Whittaker, E. T.; Watson, G. N.: A course of modern analysis. (1935) · Zbl 45.0433.02