## Abstract

Let x _{0} , x _{1} , . . ., x _{n} ∈ ℝ, be pairwise disjoint, and let θ _{0} , θ _{1} , . . ., θ _{n} ∈ Set θ := Σ _{ν=0} ^{n} θ _{ν} . For each pair j, p such that 0 ≤ j ≤ n and 0 ≤ p ≤ θ _{j} -1, let y _{j,p} be a complex number. Then there is a unique polynomial, H(x), of degree θ - 1, such that H ^{(p)} (x _{j} ) = y _{j,p} , for 0 ≤ p ≤ θ _{j} - 1, 0 ≤ j ≤ n. In particular, there is a unique fundamental Hermite polynomial, T _{j,p} (x), of degree θ - 1, such that T _{j,p} ^{(r)} (x _{s} ) = δ _{j,s} δ _{p,r} , 0 ≤ r ≤ θ _{s} - 1, 0 ≤ s ≤ n, δ being Kronecker's delta, and we have the representation. We give an explicit representation of the polynomials T _{j,p} (x).

Original language | English |
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Pages (from-to) | 147-153 |

Number of pages | 7 |

Journal | Jaen Journal on Approximation |

Volume | 10 |

Issue number | 1 |

State | Published - 1 Dec 2018 |

## Keywords

- Explicit representation of the fundamental polynomials
- Hermite interpolation