A new matrix inverse

We compute the inverse of a specific infinite-dimensional matrix, thus unifying a number of previous matrix inversions. Our inversion theorem is applied to derive a number of summation formulas of hypergeometric type.

[1]  Mizan Rahman,et al.  Basic Hypergeometric Series , 1990 .

[2]  G. Egorychev.  Integral representation and the computation of combinatorial sums , 1984 .

[3]  A new convolution formula and some new orthogonal relations for inversion of series , 1962 .

[4]  W. N. Bailey.  Some Identities in Combinatory Analysis , 1946 .

[5]  Mizan Rahman.  Some Quadratic and Cubic Summation Formulas for Basic Hypergeometric Series , 1993, Canadian Journal of Mathematics.

[6]  H. Gould.  A series transformation for finding convolution identities , 1961 .

[7]  H. Gould.  Inverse series relations and other expansions involving Humbert polynomials , 1965 .

[8]  Ira M. Gessel,et al.  Applications of q-lagrange inversion to basic hypergeometric series , 1983 .

[9]  T. Koornwinder,et al.  BASIC HYPERGEOMETRIC SERIES (Encyclopedia of Mathematics and its Applications) , 1991 .

[10]  Mizan Rahman,et al.  An Indefinite Bibasic Summation Formula and Some Quadratic, Cubic and Quartic Summation and Transformation Formulas , 1990, Canadian Journal of Mathematics.

[11]  A. Verma,et al.  Transformations of non-terminating basic hypergeometric series, their contour integrals and applications to Rogers-Ramanujan identities , 1982 .

[12]  H. W. Gould,et al.  Some new inverse series relations , 1973 .

[13]  C. Krattenthaler.  Operator methods and Lagrange inversion: a unified approach to Lagrange formulas , 1988 .

[14]  David M. Bressoud,et al.  Some identities for terminating q-series , 1981, Mathematical Proceedings of the Cambridge Philosophical Society.

[15]  L. Carlitz,et al.  Some inverse relations , 1973 .

[16]  B. Dwork.  Generalized Hypergeometric Functions , 1990 .

[17]  George Gasper,et al.  Summation, transformation, and expansion formulas for bibasic series , 1989 .