connection%20formulas%20across%20transition%20points
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11—20 of 396 matching pages
11: Bibliography K
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Connection formulae for the first Painlevé transcendent in the complex domain.
Lett. Math. Phys. 27 (4), pp. 243–252.
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Connecting Jacobi elliptic functions with different modulus parameters.
Pramana 63 (5), pp. 921–936.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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12: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics.
Comput. Phys. Comm. 150 (1), pp. 1–20.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Special value of the hypergeometric function and connection formulae among asymptotic expansions.
J. Indian Math. Soc. (N.S.) 51, pp. 161–221.
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13: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems.
Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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A connection formula for the -confluent hypergeometric function.
SIGMA Symmetry Integrability Geom. Methods Appl. 9, pp. Paper 050, 13.
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14: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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Mathieu functions of general order: Connection formulae, base functions and asymptotic formulae. I–V.
Philos. Trans. Roy. Soc. London Ser. A 301, pp. 75–162.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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The double confluent Heun equation: Characteristic exponent and connection formulae.
Methods Appl. Anal. 1 (3), pp. 348–370.
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15: 12.16 Mathematical Applications
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►PCFs are used as basic approximating functions in the theory of contour integrals with a coalescing saddle point and an algebraic singularity, and in the theory of differential equations with two coalescing turning points; see §§2.4(vi) and 2.8(vi).
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►In Brazel et al. (1992) exponential asymptotics are considered in connection with an eigenvalue problem involving PCFs.
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►PCFs are also used in integral transforms with respect to the parameter, and inversion formulas exist for kernels containing PCFs.
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16: 26.2 Basic Definitions
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►A k-dimensional lattice path is a directed path composed of segments that connect vertices in so that each segment increases one coordinate by exactly one unit.
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17: 2.11 Remainder Terms; Stokes Phenomenon
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§2.11(ii) Connection Formulas
… ►However, on combining (2.11.6) with the connection formula (8.19.18), with , we derive … ►However, to enjoy the resurgence property (§2.7(ii)) we often seek instead expansions in terms of the -functions introduced in §2.11(iii), leaving the connection of the error-function type behavior as an implicit consequence of this property of the -functions. … ►In this connection see also Byatt-Smith (2000). … ►For example, using double precision is found to agree with (2.11.31) to 13D. …18: Bibliography C
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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A connection formula for the second Painlevé transcendent.
Arch. Rational Mech. Anal. 103 (2), pp. 97–138.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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An approximation connected with
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Proc. Edinburgh Math. Soc. (2) 3, pp. 201–206.
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19: 31.18 Methods of Computation
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►Subsequently, the coefficients in the necessary connection formulas can be calculated numerically by matching the values of solutions and their derivatives at suitably chosen values of ; see Laĭ (1994) and Lay et al. (1998).
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20: 8 Incomplete Gamma and Related
Functions
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