Geodesic
Extensions of Vandermonde Type Convolutions with Several Summations and their Applications - I
Canadian mathematical bulletin, Tome 12 (1969) no. 1, pp. 45-62

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In an earlier paper [8], one of the authors has established some Vandermonde type convolution identities involving multinomial coefficients with several summations which evidently are regeneralizations of identities in [1] with one summation. In this paper similar identities are derived for coefficients (defined below) of a general type, in the line of the results in [2] and [3], Furthermore, in a series of papers [4], [5], [6], Gould has obtained results on inversion of series and on classical polynomials by an extensive use of these identities with one summation. 
Mohanty, S.G.; Handa, B.R. Extensions of Vandermonde Type Convolutions with Several Summations and their Applications - I. Canadian mathematical bulletin, Tome 12 (1969) no. 1, pp. 45-62. doi: 10.4153/CMB-1969-006-4
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[1] 1. Gould, H. W., Some generalizations of Vandermonde's convolution. Amer. Math. Monthly 63 (1956) 84–91. Google Scholar

[2] 2. Gould, H. W., Final analysis of Vandermonde's convolution. Amer. Math. Monthly 64 (1957) 409–415. Google Scholar

[3] 3. Gould, H. W., Generalization of a theorem of Jensen concerning convolutions. Duke Math. J. 27 (1960) 71–76. Google Scholar

[4] 4. Gould, H. W., A series transformation for finding convolution identities. Duke Math. J. 28 (1961) 193–202. Google Scholar

[5] 5. Gould, H. W., A new convolution formula and some new orthogonal relations for inversion of series. Duke Math. J. 29 (1962) 393–404. Google Scholar

[6] 6. Gould, H. W., Generalization of an integral formula of Bateman. Duke Math. J. 29 (1962) 475–479. Google Scholar

[7] 7. Goursat, E., A course in mathematical analysis, Vol. II, Part 1 (Dover, New York, 1959). Google Scholar

[8] 8. Mohanty, S. G., Some convolutions with multinomial coefficients and related probability distributions. SIAM Review 8 (1966) 501–509. Google Scholar

[9] 9. Skalsky, M., A note on a convolution-type combinatorial identity. Amer. Math. Monthly, 74 (1967) 836–838. Google Scholar

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