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10 matching pages
1: 20.11 Generalizations and Analogs
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§20.11(iv) Theta Functions with Characteristics
►Multidimensional theta functions with characteristics are defined in §21.2(ii) and their properties are described in §§21.3(ii), 21.5(ii), and 21.6. …2: Bibliography L
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Algorithm 917: complex double-precision evaluation of the Wright function.
ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
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Algorithm 537: Characteristic values of Mathieu’s differential equation.
ACM Trans. Math. Software 5 (1), pp. 112–117.
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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3: 28.16 Asymptotic Expansions for Large
4: Bibliography N
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Tables Relating to Mathieu Functions: Characteristic Values, Coefficients, and Joining Factors.
2nd edition, National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C..
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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5: 28.35 Tables
§28.35 Tables
… ►Ince (1932) includes eigenvalues , , and Fourier coefficients for or , ; 7D. Also , for , , corresponding to the eigenvalues in the tables; 5D. Notation: , .
Kirkpatrick (1960) contains tables of the modified functions , for , , ; 4D or 5D.
National Bureau of Standards (1967) includes the eigenvalues , for with , and with ; Fourier coefficients for and for , , respectively, and various values of in the interval ; joining factors , for with (but in a different notation). Also, eigenvalues for large values of . Precision is generally 8D.
Blanch and Clemm (1969) includes eigenvalues , for , , , ; 4D. Also and for , , and , respectively; 8D. Double points for ; 8D. Graphs are included.
6: 28.8 Asymptotic Expansions for Large
7: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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Characteristic values of the integral equation satisfied by the Mathieu functions and its application to a system with chirality-pair interaction on a one-dimensional lattice.
Phys. A 190 (3-4), pp. 346–362.
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8: 28.1 Special Notation
9: 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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Frequency response characteristics of the multiport planar elliptic patch.
IEEE Trans. Microwave Theory Tech. 40 (8), pp. 1726–1730.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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10: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Mathieu’s Equation for Complex Parameters. Tables of Characteristic Values.
U.S. Government Printing Office, Washington, D.C..
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Table of characteristic values of Mathieu’s equation for large values of the parameter.
J. Washington Acad. Sci. 45 (6), pp. 166–196.
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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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