## A System of Orthogonal Polynomials |

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### Contents

A Generating Function | 3 |

Explicit Representation of PxfSy | 5 |

k Nature of the Spectrum | 6 |

6 other sections not shown

### Common terms and phrases

9 ds analytic continuation Approved Associated Polynomials Asymptotic Expansions bution checks COMMITTEE considering the analytic constant constant in x continuation of m(x continuous density defined determine the Jumps Differentiating discrete points discussed distri distribution if(x easily seen equation in 8.1 expanded fact following section formulas relating give given Graduate Division greater than zero Hence s2 Higher Transcendental Functions integral representation interchanging interval Jump function Legendre polynomials Let us consider main contribution Math McGraw-Hill McGregor Meixner polynomial n=o n=o neighborhood non-zero normalized obtain the Stieltjes obtained in section ORTHOGONAL POLYNOMIALS Pn(x point spectrum QQ(x radius of convergence Random Walks recurrence relation residue of m(x respect roots satisfies the third simple pole Sl-s Sl,k spectral measure Stieltjes transform Substituting SYSTEM OF ORTHOGONAL third equation ultraspherical polynomial York