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

MSC:
34M99Differential equations in the complex domain
34A30Linear ODE and systems, general
15A03Vector spaces, linear dependence, rank
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Full Text: DOI
References:
[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