Modern physics letters A, ISSN 1793-6632, 2017, Volume 32, Issue 32, p. 1750174

...(1)-gauge invariant Dirac equation is expressed in terms of Laguerre polynomials and Mathieu’s functions of complex parameter...

Mathieu's functions | Dirac equation | Magnetars | INTEGER ORDERS | PHYSICS, NUCLEAR | COMPUTATION | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS

Mathieu's functions | Dirac equation | Magnetars | INTEGER ORDERS | PHYSICS, NUCLEAR | COMPUTATION | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS

Journal Article

ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS, ISSN 1095-0761, 2017, Volume 21, Issue 3, pp. 655 - 681

A closed expression is given for the generating function of (virtual) Poincare polynomials of moduli spaces of semi-stable sheaves on the projective plane P-2 with arbitrary rank r and Chern classes...

FORMS | STABLE SHEAVES | BETTI NUMBERS | RANK-2 | INVARIANTS | MATHIEU-GROUP | RULED SURFACE | S-DUALITY | MODULI SPACE | PHYSICS, MATHEMATICAL | VECTOR-BUNDLES | PHYSICS, PARTICLES & FIELDS

FORMS | STABLE SHEAVES | BETTI NUMBERS | RANK-2 | INVARIANTS | MATHIEU-GROUP | RULED SURFACE | S-DUALITY | MODULI SPACE | PHYSICS, MATHEMATICAL | VECTOR-BUNDLES | PHYSICS, PARTICLES & FIELDS

Journal Article

1980, Lecture notes in mathematics, ISBN 0387102825, Volume 837., vii, 126

Book

Symmetry (Basel), ISSN 2073-8994, 2019, Volume 11, Issue 9, p. 1172

.... Such fields are characterized in terms of the Mathieu functions. We show that the regions of stability of the Mathieu functions determine the nature of the driving fields...

PHASE | time-dependent driving fields | EVOLUTION | Mathieu functions | QUANTUM | MULTIDISCIPLINARY SCIENCES | quantum control

PHASE | time-dependent driving fields | EVOLUTION | Mathieu functions | QUANTUM | MULTIDISCIPLINARY SCIENCES | quantum control

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 2006, Volume 19, Issue 10, pp. 1073 - 1077

...–Hauss complete real-parameter Omega function Ω ( w ) , which is associated with the complex-index Bernoulli function B α ( z...

Bessel function | Butzer–Flocke–Hauss complete Omega function | Complex-index Euler function | Alternating Mathieu series | Complex-index Bernoulli function | Riemann’s Zeta function | Integral representations of alternating Mathieu series | Integral representation of the Omega function | Dirichlet’s Eta function | Butzer-Flocke-Hauss complete Omega function | Dirichlet's Eta function | Riemann's Zeta function | MATHEMATICS, APPLIED | integral representation of the Omega factor | complete-index Euler function | integral representations of alternating Mathieu series | alternating Mathieu series

Bessel function | Butzer–Flocke–Hauss complete Omega function | Complex-index Euler function | Alternating Mathieu series | Complex-index Bernoulli function | Riemann’s Zeta function | Integral representations of alternating Mathieu series | Integral representation of the Omega function | Dirichlet’s Eta function | Butzer-Flocke-Hauss complete Omega function | Dirichlet's Eta function | Riemann's Zeta function | MATHEMATICS, APPLIED | integral representation of the Omega factor | complete-index Euler function | integral representations of alternating Mathieu series | alternating Mathieu series

Journal Article

Optics Communications, ISSN 0030-4018, 08/2015, Volume 349, pp. 185 - 192

Elliptic Cylindrical Waves (ECW), defined as the product of an angular Mathieu function by its corresponding radial Mathieu function, occur in the solution...

Plane surface | Plane-wave spectrum | Fourier integral | Mathieu functions | Elliptic cylinder | CIRCULAR-CYLINDER | SPHERE | SURFACE | LOSSY MEDIA | OPTICS | SCATTERING

Plane surface | Plane-wave spectrum | Fourier integral | Mathieu functions | Elliptic cylinder | CIRCULAR-CYLINDER | SPHERE | SURFACE | LOSSY MEDIA | OPTICS | SCATTERING

Journal Article

ACM Transactions on Mathematical Software (TOMS), ISSN 0098-3500, 09/2013, Volume 40, Issue 1, pp. 1 - 19

Software to compute angular and radial Mathieu functions is provided in the case that the parameter q is a complex variable and the independent variable x is real...

special function | Mathieu function | validation | computation | Validation | Special function | Computation | MATHEMATICS, APPLIED | SERIES | CYLINDER | DIFFERENTIAL-EQUATION | EXACT RADIATION | PENETRATION | NONINTEGER | COMPUTER SCIENCE, SOFTWARE ENGINEERING | EIGENVALUES | INTERFACE | ELECTROMAGNETIC SCATTERING | Algorithms | Functional equations | Engineering research | Functions | Mathematical software | Research | Methods | Complex variables

special function | Mathieu function | validation | computation | Validation | Special function | Computation | MATHEMATICS, APPLIED | SERIES | CYLINDER | DIFFERENTIAL-EQUATION | EXACT RADIATION | PENETRATION | NONINTEGER | COMPUTER SCIENCE, SOFTWARE ENGINEERING | EIGENVALUES | INTERFACE | ELECTROMAGNETIC SCATTERING | Algorithms | Functional equations | Engineering research | Functions | Mathematical software | Research | Methods | Complex variables

Journal Article

1971, Pure and applied mathematics, ISBN 9780471401704, Volume 23., xi, 322

Book

Reports on Mathematical Physics, ISSN 0034-4877, 02/2017, Volume 79, Issue 1, pp. 81 - 87

After a brief introduction to Heun type functions we note that the actual solutions of the eigenvalue equation emerging in the calculation of the one-loop contribution to QCD from the Belavin—Polyakov—Schwarz...

quantum field theory | Heun functions | Dirac equation | INSTANTONS | PHYSICS, MATHEMATICAL | WAVE-EQUATIONS | ROTATING BLACK-HOLES | MATHIEU FUNCTIONS

quantum field theory | Heun functions | Dirac equation | INSTANTONS | PHYSICS, MATHEMATICAL | WAVE-EQUATIONS | ROTATING BLACK-HOLES | MATHIEU FUNCTIONS

Journal Article

1967, 2d ed., xlvii, 311

Book

1964, Unabridged and corr. --, Dover books on engineering and engineering physics, xii, 401 p. illus.

Book

1951, xlvii, 278

Book

Journal of mathematical analysis and applications, ISSN 0022-247X, 2018, Volume 468, Issue 2, pp. 650 - 673

...–Wright functions. In particular, we give new Laplace and Stieltjes transforms for this special function under some restrictions on parameters...

Generalized Stieltjes function | Turán type inequalities | Mathieu-type series | Fox's H-function | Complete monotonicity | Fox–Wright function | Fox-Wright function | MATHEMATICS | Turan type inequalities | MATHEMATICS, APPLIED | INEQUALITIES | SERIES | GAMMA-FUNCTION

Generalized Stieltjes function | Turán type inequalities | Mathieu-type series | Fox's H-function | Complete monotonicity | Fox–Wright function | Fox-Wright function | MATHEMATICS | Turan type inequalities | MATHEMATICS, APPLIED | INEQUALITIES | SERIES | GAMMA-FUNCTION

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 11/2015, Volume 11

...], uniform asymptotic approximations are obtained in the first part of this paper for the Lame and Mathieu functions with a large real parameter...

Lamé functions | Mathieu functions | Coalescing turning points | Uniform asymptotic approximations | Lame functions | uniform asymptotic approximations | ELLIPSOIDAL WAVE FUNCTIONS | EXPANSIONS | coalescing turning points | PHYSICS, MATHEMATICAL

Lamé functions | Mathieu functions | Coalescing turning points | Uniform asymptotic approximations | Lame functions | uniform asymptotic approximations | ELLIPSOIDAL WAVE FUNCTIONS | EXPANSIONS | coalescing turning points | PHYSICS, MATHEMATICAL

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2011, Volume 379, Issue 1, pp. 35 - 47

In this paper, an error estimate of spectral approximations by prolate spheroidal wave functions (PSWFs...

Order of convergence | Spectral approximation | Prolate spheroidal wave functions | Mathieu functions | MATHEMATICS | MATHEMATICS, APPLIED | SPECTRAL APPROXIMATIONS | SPHEROIDAL WAVE-FUNCTIONS | FOURIER-ANALYSIS

Order of convergence | Spectral approximation | Prolate spheroidal wave functions | Mathieu functions | MATHEMATICS | MATHEMATICS, APPLIED | SPECTRAL APPROXIMATIONS | SPHEROIDAL WAVE-FUNCTIONS | FOURIER-ANALYSIS

Journal Article

IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, 04/2014, Volume 62, Issue 4, pp. 2071 - 2080

A recursive solution for the computation of the two-dimensional Green's function for the multilayer elliptic cylinder is reported...

integral equations | Electromagnetic scattering | Scattering | Nonhomogeneous media | Dielectrics | Green's function methods | Mathematical model | Permittivity | Green function | Equations | nonhomogeneous media | SERIES | CIRCULAR-CYLINDER | ILLUMINATION | TELECOMMUNICATIONS | MULTILAYER | ANTENNA | MATHIEU FUNCTIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Analysis | Electromagnetic waves | Electric waves | Innovations | Electromagnetic radiation | Eigenfunctions | Mathematical models | Methods | Multilayers | Green's functions | Recursive | Two dimensional | Antennas | Cylinders

integral equations | Electromagnetic scattering | Scattering | Nonhomogeneous media | Dielectrics | Green's function methods | Mathematical model | Permittivity | Green function | Equations | nonhomogeneous media | SERIES | CIRCULAR-CYLINDER | ILLUMINATION | TELECOMMUNICATIONS | MULTILAYER | ANTENNA | MATHIEU FUNCTIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Analysis | Electromagnetic waves | Electric waves | Innovations | Electromagnetic radiation | Eigenfunctions | Mathematical models | Methods | Multilayers | Green's functions | Recursive | Two dimensional | Antennas | Cylinders

Journal Article

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