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Dutch literature --- 684.94 --- Legendre, Marc --- graphic novels --- striptekenen --- stripverhalen --- het boek, boekillustratie --- Comics
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799.95 --- Legendre, Marc --- Dutch literature --- 684.94 --- graphic novels --- striptekenen --- stripverhalen --- het boek, boekillustratie --- 891 --- auteursstrips --- bandes dessinées d_auteur
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517.58 --- Academic collection --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Theses --- 517.58 Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials.
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Elliptic functions --- Fonctions elliptiques --- 517.58 --- Elliptic integrals --- Functions, Elliptic --- Integrals, Elliptic --- Transcendental functions --- Functions of complex variables --- Integrals, Hyperelliptic --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Elliptic functions. --- 517.58 Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials --- Fonctions elliptiques. --- Functies (Elliptische).
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Harmonic analysis. Fourier analysis --- Orthogonal polynomials --- Asymptotic theory --- 517.58 --- #WWIS:ANAL --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Asymptotic theory. --- 517.58 Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials.
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Numerical solutions of algebraic equations --- 517.58 --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Interval analysis (Mathematics) --- Iterative methods (Mathematics) --- Polynomials. --- Interval analysis (Mathematics). --- Iterative methods (Mathematics). --- 517.58 Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials.
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Mathematical physics --- Painlevé equations --- Physique mathématique --- Asymptotic theory --- Congresses --- Théorie asymptotique --- Congrès --- Painleve equations --- 517.1 --- 517.58 --- Physical mathematics --- Physics --- Equations, Painlevé --- Functions, Painlevé --- Painlevé functions --- Painlevé transcendents --- Transcendents, Painlevé --- Differential equations, Nonlinear --- Introduction to analysis --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Mathematics --- 517.58 Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- 517.1 Introduction to analysis --- Painlevé equations --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials --- Painleve equations - Congresses. --- Mathematical physics - Asymptotic theory - Congresses.
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Orthogonale rationale functies (ORFs) met vaste polen vormen een natuurlijke veralgemening van orthogonale veeltermen. Talrijke resultaten zijn reeds veralgemeend naar het rationale geval, maar er zijn weinig gevallen waarin expliciete uitdrukkingen gekend zijn voor ORFs. Tevens beperkte het onderzoek van ORFs op een deelset van de reë le as zich tot nu toe voornamelijk tot het geval van rationale functies met reële polen. In het eerste deel van deze thesis leiden we nieuwe expliciete uitdrukkingen af voor ORFs en veralgemenen we bestaande uitdrukkingen naar het geval van willekeurig complexe polen. Vervolgens gebruiken we deze uitdrukkingen om vergelijkingen te bekomen voor de knooppunten en gewichten in rationale kwadratuurformules overeenkomstig de Chebyshev gewichtsfuncties op de complexe eenheidscirkel en op het interval. In het tweede deel veralgemenen we de drie-term recursiebetrekking voor ORFs op een deelset van de reële as naar het geval van willekeurig complexe polen en geven we een Favard-type stelling voor rationale functies gegenereerd door een dergelijke drie-term recursiebetrekking. Als toepassing bestuderen we geassocieerde rationale functies gebaseerd op de drie-term recursiebetrekking met verschoven recursie-coëfficiënten. Vervolgens bewijzen we een relatie tussen ORFs op de complexe eenheidscirkel en op het interval. Om dit gedeelte af te sluiten gebruiken we deze relatie dan om verschillende soorten convergentie te onderzoeken en om asymptotische formules af te leiden voor de recursie-coëfficiënten, voor de ORFs op het interval. Tot slot bestuderen we in het laatste deel van deze thesis het verband tussen ORFs en de rationale Lanczos methode voor Hermitische matrices. Orthogonal rational functions (ORFs) with prescribed poles are a natural generalization of orthogonal polynomials. Many results have already been generalized to the rational case. However, there are less cases in which explicit expressions are known for the ORFs. Moreover, the theory of orthogonality on a subset of the real line has so far been restricted to the case of rational functions with all real poles. In the first part of this thesis, we derive new explicit expressions for ORFs and extend existing expressions to the case of arbitrary complex poles. We then use these expressions to obtain equations for the nodes and weights in rational quadrature formulas associated with the Chebyshev weight functions on the unit circle and on the interval. In the second part, we generalize the three-term recurrence for ORFs on a subset of the real line to the case of arbitrary complex poles, and give a Favard-type theorem for rational functions generated by such a three-term recurrence. As an application, we study associated rational functions based on the three-term recurrence with shifted recurrence coefficients. Next, we prove a relation between ORFs on the unit circle and on the interval. To conclude this part, we then use this relation to study different types of convergence, and to derive asymptotic formulas for the recurrence coefficients, for ORFs on the interval. Finally, in the last part of this thesis we study the relation between ORFs and the rational Lanczos method for Hermitian matrices. Orthogonale rationale functies (ORFs) met vaste polen vormen een natuurlijke veralgemening van orthogonale veeltermen. Talrijke resultaten zijn reeds veralgemeend naar het rationale geval, maar er zijn weinig gevallen waarin expliciete uitdrukkingen gekend zijn voor ORFs. Tevens beperkte het onderzoek van ORFs op een deelset van de reële as zich tot nu toe voornamelijk tot het geval van rationale functies met reële polen. In het eerste deel van deze thesis leiden we nieuwe expliciete uitdrukkingen af voor ORFs en veralgemenen we bestaande uitdrukkingen naar het geval van willekeurig complexe polen. Vervolgens gebruiken we deze uitdrukkingen om vergelijkingen te bekomen voor de knooppunten en gewichten in rationale kwadratuurformules overeenkomstig de Chebyshev gewichtsfuncties op de complexe eenheidscirkel en op het interval. In het tweede deel veralgemenen we de drie-term recursiebetrekking voor ORFs op een deelset van de reële as naar het geval van willekeurig complexe polen en geven we een Favard-type stelling voor rationale functies gegenereerd door een dergelijke drie-term recursiebetrekking. Als toepassing bestuderen we geassocieerde rationale functies gebaseerd op de drie-term recursiebetrekking met verschoven recursie-coëfficiënten. Vervolgens bewijzen we een relatie tussen ORFs op de complexe eenheidscirkel en op het interval. Om dit gedeelte af te sluiten gebruiken we deze relatie dan om verschillende soorten convergentie te onderzoeken en om asymptotische formules af te leiden voor de recursie-coëfficiënten, voor de ORFs op het interval. Tot slot bestuderen we in het laatste deel van deze thesis het verband tussen ORFs en de rationale Lanczos methode voor Hermitische matrices.
517.58 <043> --- 519.64 <043> --- 519.65 <043> --- Academic collection --- 681.3*G<043> --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials.--Dissertaties --- Numerical methods for solution of integral equations. Quadrature formulae--Dissertaties --- Approximation. Interpolation--Dissertaties --- Mathematics of computing--Dissertaties --- Theses --- 517.58 <043> Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials.--Dissertaties
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Mathématiques --- Wiskunde --- Academic collection --- 517.93 --- homogeen --- Laplace transformatie --- delta --- randvoorwaarde --- sturm-liouvilleprobleem --- lineair --- euler --- legendre --- transformaties --- Fourier --- differentiaalvergelijkingen --- orde --- bessel --- convolutie --- reeksen --- Special differential equations. Systems of analytic mechanics, automatic control, operators. Dynamic systems --- 517.93 Special differential equations. Systems of analytic mechanics, automatic control, operators. Dynamic systems
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This book introduces new methods in the theory of partial differential equations derivable from a Lagrangian. These methods constitute, in part, an extension to partial differential equations of the methods of symplectic geometry and Hamilton-Jacobi theory for Lagrangian systems of ordinary differential equations. A distinguishing characteristic of this approach is that one considers, at once, entire families of solutions of the Euler-Lagrange equations, rather than restricting attention to single solutions at a time. The second part of the book develops a general theory of integral identities, the theory of "compatible currents," which extends the work of E. Noether. Finally, the third part introduces a new general definition of hyperbolicity, based on a quadratic form associated with the Lagrangian, which overcomes the obstacles arising from singularities of the characteristic variety that were encountered in previous approaches. On the basis of the new definition, the domain-of-dependence theorem and stability properties of solutions are derived. Applications to continuum mechanics are discussed throughout the book. The last chapter is devoted to the electrodynamics of nonlinear continuous media.
Differentiaalvergelijkingen [Hyperbolische ] --- Differential equations [Hyperbolic] --- Equations différentielles hyperboliques --- Symplectic manifolds --- Differential equations, Hyperbolic. --- Symplectic manifolds. --- Variétés symplectiques --- Equations différentielles hyperboliques --- Variétés symplectiques --- Manifolds, Symplectic --- Geometry, Differential --- Manifolds (Mathematics) --- Hyperbolic differential equations --- Differential equations, Partial --- Action (physics). --- Boundary value problem. --- Canonical form. --- Causal structure. --- Classical mechanics. --- Complex analysis. --- Configuration space. --- Conservative vector field. --- Conserved current. --- Conserved quantity. --- Continuum mechanics. --- Derivative. --- Diffeomorphism. --- Differentiable manifold. --- Differential geometry. --- Dimension. --- Dimensional analysis. --- Dirichlet's principle. --- Einstein field equations. --- Electromagnetic field. --- Equation. --- Equations of motion. --- Equivalence class. --- Error term. --- Euclidean space. --- Euler system. --- Euler's equations (rigid body dynamics). --- Euler–Lagrange equation. --- Existence theorem. --- Existential quantification. --- Exponential map (Lie theory). --- Exponential map (Riemannian geometry). --- Exterior derivative. --- Fiber bundle. --- Foliation. --- Fritz John. --- General relativity. --- Hamiltonian mechanics. --- Hamilton–Jacobi equation. --- Harmonic map. --- Hessian matrix. --- Holomorphic function. --- Hyperbolic partial differential equation. --- Hyperplane. --- Hypersurface. --- Identity element. --- Iteration. --- Iterative method. --- Lagrangian (field theory). --- Lagrangian. --- Legendre transformation. --- Lie algebra. --- Linear approximation. --- Linear differential equation. --- Linear map. --- Linear span. --- Linearity. --- Linearization. --- Maximum principle. --- Maxwell's equations. --- Nonlinear system. --- Open set. --- Ordinary differential equation. --- Orthogonal complement. --- Parameter. --- Partial differential equation. --- Phase space. --- Pointwise. --- Poisson bracket. --- Polynomial. --- Principal part. --- Principle of least action. --- Probability. --- Pullback bundle. --- Pullback. --- Quadratic form. --- Quantity. --- Requirement. --- Riemannian manifold. --- Second derivative. --- Simultaneous equations. --- Special case. --- State function. --- Stokes' theorem. --- Subset. --- Surjective function. --- Symplectic geometry. --- Tangent bundle. --- Tangent vector. --- Theorem. --- Theoretical physics. --- Theory. --- Underdetermined system. --- Variable (mathematics). --- Vector bundle. --- Vector field. --- Vector space. --- Volume form. --- Zero of a function. --- Zero set.
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