Liouville%20function
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7 matching pages
1: 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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Sturm-Liouville Theory.
Birkhäuser Verlag, Basel.
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2: 27.2 Functions
§27.2 Functions
… ►Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes. … ►This is Jordan’s function. … ►This is Liouville’s function. … ►This is Mangoldt’s function. …3: Bibliography D
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Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann.
Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).
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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
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Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Convergent Liouville-Green expansions for second-order linear differential equations, with an application to Bessel functions.
Proc. Roy. Soc. London Ser. A 440, pp. 37–54.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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4: 3.8 Nonlinear Equations
§3.8 Nonlinear Equations
… ►§3.8(v) Zeros of Analytic Functions
… ►For describing the distribution of complex zeros of solutions of linear homogeneous second-order differential equations by methods based on the Liouville–Green (WKB) approximation, see Segura (2013). … ►Consider and . We have and . …5: Bibliography S
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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Liouville-Green approximations via the Riccati transformation.
J. Math. Anal. Appl. 116 (1), pp. 147–165.
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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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6: Bibliography G
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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Mathieu functions.
Trans. Camb. Philos. Soc. 23, pp. 303–336.
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An extended class of orthogonal polynomials defined by a Sturm-Liouville problem.
J. Math. Anal. Appl. 359 (1), pp. 352–367.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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7: Bibliography B
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A program for computing the Riemann zeta function for complex argument.
Comput. Phys. Comm. 20 (3), pp. 441–445.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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A short table of the functions
, from to
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Phil. Mag. Series 7 20, pp. 343–347.
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Bessel functions and modular relations of higher type and hyperbolic differential equations.
Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.
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A Sturm-Liouville eigenproblem of the fourth kind: A critical latitude with equatorial trapping.
Stud. Appl. Math. 101 (4), pp. 433–455.
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