Add to ORKGFor any univariate polynomial P whose coefficients lie in an ordinary differential field F of characteristic zero, and for any constant indeterminate α, there exists a nonunique nonzero linear ordinary differential operator R of finite order such that the αth power of each root of P is a solution of Rzα = 0, and the coefficient functions of R all lie in the differential ring generated by the coefficients of P and the integers Z. We call R an α-resolvent of P. The author’s powersum formula yields one particular α-resolvent. However, this formula yields extremely large polynomials in the coefficients of P and their derivatives. We will use the A-hypergeometric linear partial differential equations of Mayr and Gelfand to find a particular fact...
Let {P n(x)} n=0∞ be a sequence of polynomials of degree n. We define two sequences of differential ...
Contains fulltext : 28569.pdf (Publisher’s version ) (Open Access
Consider two differential operators L1 = � aid i and L2 = � bjd j with coefficients in a different...
For any univariate polynomial P whose coefficients lie in an ordinary differential field F of charac...
For any univariate polynomial P whose coefficients lie in an ordinary differential field F of charac...
For any univariate polynomial P whose coefficients lie in an ordinary differential field of charact...
We will prove that we can specialize the indeterminate α in a linear differential α-resolvent of a u...
We will prove that we can specialize the indeterminate α in a linear differential α-resolvent of a u...
We prove that the author’s powersum formula yields a nonzero expression for a partic-ular linear ord...
We prove that the author’s powersum formula yields a nonzero expression for a partic-ular linear ord...
We prove that the author’s powersum formula yields a nonzero expression for a partic-ular linear ord...
We prove that the author's powersum formula yields a nonzero expression for a particular linear ordi...
We will determine the number of powers of α that appear with nonzero coefficient in an α-power linea...
AbstractFor any univariate polynomial with coefficients in a differential field of characteristic ze...
Abstract The existence of linear differential resolvents for zα for any root z of an ordinary polyno...
Let {P n(x)} n=0∞ be a sequence of polynomials of degree n. We define two sequences of differential ...
Contains fulltext : 28569.pdf (Publisher’s version ) (Open Access
Consider two differential operators L1 = � aid i and L2 = � bjd j with coefficients in a different...
For any univariate polynomial P whose coefficients lie in an ordinary differential field F of charac...
For any univariate polynomial P whose coefficients lie in an ordinary differential field F of charac...
For any univariate polynomial P whose coefficients lie in an ordinary differential field of charact...
We will prove that we can specialize the indeterminate α in a linear differential α-resolvent of a u...
We will prove that we can specialize the indeterminate α in a linear differential α-resolvent of a u...
We prove that the author’s powersum formula yields a nonzero expression for a partic-ular linear ord...
We prove that the author’s powersum formula yields a nonzero expression for a partic-ular linear ord...
We prove that the author’s powersum formula yields a nonzero expression for a partic-ular linear ord...
We prove that the author's powersum formula yields a nonzero expression for a particular linear ordi...
We will determine the number of powers of α that appear with nonzero coefficient in an α-power linea...
AbstractFor any univariate polynomial with coefficients in a differential field of characteristic ze...
Abstract The existence of linear differential resolvents for zα for any root z of an ordinary polyno...
Let {P n(x)} n=0∞ be a sequence of polynomials of degree n. We define two sequences of differential ...
Contains fulltext : 28569.pdf (Publisher’s version ) (Open Access
Consider two differential operators L1 = � aid i and L2 = � bjd j with coefficients in a different...