Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case. J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin & P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis.

Orthogonal polynomials --- Asymptotic theory --- Orthogonal polynomials -- Asymptotic theory. --- Polynomials. --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Asymptotic theory. --- Asymptotic theory of orthogonal polynomials --- Algebra --- Airy function. --- Analytic continuation. --- Analytic function. --- Ansatz. --- Approximation error. --- Approximation theory. --- Asymptote. --- Asymptotic analysis. --- Asymptotic expansion. --- Asymptotic formula. --- Beta function. --- Boundary value problem. --- Calculation. --- Cauchy's integral formula. --- Cauchy–Riemann equations. --- Change of variables. --- Complex number. --- Complex plane. --- Correlation function. --- Degeneracy (mathematics). --- Determinant. --- Diagram (category theory). --- Discrete measure. --- Distribution function. --- Eigenvalues and eigenvectors. --- Equation. --- Estimation. --- Existential quantification. --- Explicit formulae (L-function). --- Factorization. --- Fredholm determinant. --- Functional derivative. --- Gamma function. --- Gradient descent. --- Harmonic analysis. --- Hermitian matrix. --- Homotopy. --- Hypergeometric function. --- I0. --- Identity matrix. --- Inequality (mathematics). --- Integrable system. --- Invariant measure. --- Inverse scattering transform. --- Invertible matrix. --- Jacobi matrix. --- Joint probability distribution. --- Lagrange multiplier. --- Lax equivalence theorem. --- Limit (mathematics). --- Linear programming. --- Lipschitz continuity. --- Matrix function. --- Maxima and minima. --- Monic polynomial. --- Monotonic function. --- Morera's theorem. --- Neumann series. --- Number line. --- Orthogonal polynomials. --- Orthogonality. --- Orthogonalization. --- Parameter. --- Parametrix. --- Pauli matrices. --- Pointwise convergence. --- Pointwise. --- Polynomial. --- Potential theory. --- Probability distribution. --- Probability measure. --- Probability theory. --- Probability. --- Proportionality (mathematics). --- Quantity. --- Random matrix. --- Random variable. --- Rate of convergence. --- Rectangle. --- Rhombus. --- Riemann surface. --- Special case. --- Spectral theory. --- Statistic. --- Subset. --- Theorem. --- Toda lattice. --- Trace (linear algebra). --- Trace class. --- Transition point. --- Triangular matrix. --- Trigonometric functions. --- Uniform continuity. --- Unit vector. --- Upper and lower bounds. --- Upper half-plane. --- Variational inequality. --- Weak solution. --- Weight function. --- Wishart distribution. --- Orthogonal polynomials - Asymptotic theory

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Carcinogenesis --- Cancer --- Disease Susceptibility --- Cells --- Age Factors --- Diseases --- Genotype --- Gene Expression Regulation --- Genetic Processes --- Epidemiologic Factors --- Anatomy --- Genetic Phenomena --- Disease Attributes --- Pathologic Processes --- Phenomena and Processes --- Quality of Health Care --- Public Health --- Environment and Public Health --- Pathological Conditions, Signs and Symptoms --- Health Care Quality, Access, and Evaluation --- Health Care --- Age of Onset --- Gene Expression Regulation, Neoplastic --- Neoplasms --- Stem Cells --- Genetic Predisposition to Disease --- Mutagenesis --- Medicine --- Health & Biological Sciences --- Oncology --- Age factors --- Genetic aspects --- Epidemiology --- Predisposition, Genetic --- Susceptibility, Genetic --- Genetic Predisposition --- Genetic Susceptibility --- Genetic Predispositions --- Genetic Susceptibilities --- Predispositions, Genetic --- Susceptibilities, Genetic --- Colony-Forming Unit --- Colony-Forming Units --- Mother Cells --- Progenitor Cells --- Cell, Mother --- Cell, Progenitor --- Cell, Stem --- Cells, Mother --- Cells, Progenitor --- Cells, Stem --- Colony Forming Unit --- Colony Forming Units --- Mother Cell --- Progenitor Cell --- Stem Cell --- Benign Neoplasms --- Malignancy --- Neoplasia --- Neoplasm --- Neoplasms, Benign --- Tumors --- Benign Neoplasm --- Cancers --- Malignancies --- Neoplasias --- Neoplasm, Benign --- Tumor --- Mutageneses --- Regulation, Gene Expression, Neoplastic --- Neoplastic Gene Expression Regulation --- Regulation of Gene Expression, Neoplastic --- Age-at-Onset --- Age at Onset --- Onset Age --- Healthcare Quality, Access, and Evaluation --- Symptoms and General Pathology --- Community-Based Distribution --- Contraceptive Distribution --- Delivery of Healthcare --- Dental Care Delivery --- Distribution, Non-Clinical --- Distribution, Nonclinical --- Distributional Activities --- Healthcare --- Healthcare Delivery --- Healthcare Systems --- Non-Clinical Distribution --- Nonclinical Distribution --- Delivery of Dental Care --- Health Care Delivery --- Health Care Systems --- Activities, Distributional --- Activity, Distributional --- Care, Health --- Community Based Distribution --- Community-Based Distributions --- Contraceptive Distributions --- Deliveries, Healthcare --- Delivery, Dental Care --- Delivery, Health Care --- Delivery, Healthcare --- Distribution, Community-Based --- Distribution, Contraceptive --- Distribution, Non Clinical --- Distributional Activity --- Distributions, Community-Based --- Distributions, Contraceptive --- Distributions, Non-Clinical --- Distributions, Nonclinical --- Health Care System --- Healthcare Deliveries --- Healthcare System --- Non Clinical Distribution --- Non-Clinical Distributions --- Nonclinical Distributions --- System, Health Care --- System, Healthcare --- Systems, Health Care --- Systems, Healthcare --- Environment, Preventive Medicine & Public Health --- Environment, Preventive Medicine and Public Health --- Health, Public --- Quality of Care --- Quality of Healthcare --- Care Qualities --- Care Quality --- Health Care Quality --- Healthcare Quality --- Pathological Processes --- Processes, Pathologic --- Processes, Pathological --- Attribute, Disease --- Attributes, Disease --- Disease Attribute --- Genetic Concepts --- Genetic Phenomenon --- Genetic Process --- Concept, Genetic --- Concepts, Genetic --- Genetic Concept --- Phenomena, Genetic --- Phenomenon, Genetic --- Process, Genetic --- Processes, Genetic --- Anatomies --- Determinant, Epidemiologic --- Determinants, Epidemiologic --- Epidemiologic Determinant --- Epidemiologic Factor --- Factor, Epidemiologic --- Factors, Epidemiologic --- Epidemiologic Determinants --- Expression Regulation, Gene --- Regulation, Gene Action --- Regulation, Gene Expression --- Gene Action Regulation --- Regulation of Gene Expression --- Genogroup --- Genogroups --- Genotypes --- Age Reporting --- Age Factor --- Factor, Age --- Factors, Age --- Cell --- Susceptibility, Disease --- Diathesis --- Diatheses --- Disease Susceptibilities --- Susceptibilities, Disease --- Carcinoma --- Malignancy (Cancer) --- Malignant tumors --- Cancer genetics --- Oncogenesis --- Pathogenesis of cancer --- Tumorigenesis --- genetics --- Pathogenesis --- Genetic Testing --- Anticipation, Genetic --- Genetic Association Studies --- Gene-Environment Interaction --- Cell Self Renewal --- Stem Cell Research --- Malignant Neoplasms --- Malignant Neoplasm --- Neoplasm, Malignant --- Neoplasms, Malignant --- Medical Oncology --- Mutation Accumulation --- Mutagens --- Mutation --- Teratogenesis --- Community Health --- Health, Community --- Preventive Medicine --- Education, Public Health Professional --- Pharmacy Audit --- Audit, Pharmacy --- Pharmacy Audits --- Molecular Biology --- RNAi Therapeutics --- Gene Regulatory Networks --- Genotyping Techniques --- Cell Biology --- Cancer genes --- Pathology --- Genetic toxicology --- Age of Onset. --- Gene Expression Regulation, Neoplastic. --- Genetic Predisposition to Disease. --- Mutagenesis. --- Stem Cells. --- etiology. --- Cancer. --- Age factors. --- Genetic aspects. --- Epidemiology.