CHEBYSHEV POLYNOMIALS

By U. NOLIE

EXERCISES REMARKS GENERALIZED HYPERGEOMETRIC FUNCTIONS; G-FUNCTIONS GENERALIZED HYPERGEOMETRIC SERIES THE GENERALIZED HYPERGEOMETRIC EQUATION MEIJER G-FUNCTIONS CHOICES OF CONTOUR OF INTEGRATION EXPANSIONS AND ASYMPTOTICS THE MELLIN TRANSFORM AND G-FUNCTIONS ASYMPTOTICS HERMITE AND PARABOLIC CYLINDER FUNCTIONS CON?UENT HYPERGEOMETRIC FUNCTIONS HYPERGEOMETRIC FUNCTIONS AND JACOBI POLYNOMIALS LEGENDRE FUNCTIONS STEEPEST DESCENTS AND STATIONARY PHASE ELLIPTIC FUNCTIONS INTEGRATION ELLIPTIC INTEGRALS JACOBI ELLIPTIC FUNCTIONS THETA FUNCTIONS JACOBI THETA FUNCTIONS AND INTEGRATION WEIERSTRASS ELLIPTIC FUNCTIONS PAINLEV´E TRANSCENDENTS THE PAINLEV´E METHOD DERIVATION OF PII SOLUTIONS OF PII COMPATIBILITY CONDITIONS AND B¨ACKLUND TRANSFORMATIONS CONSTRUCTION OF MONODROMY AND ISOMONODROMY THE INVERSE PROBLEM AND THE PAINLEV´E PROPERTY ASYMPTOTICS OF PII(0) 15 10 REMARKS