theta%20functions
(0.005 seconds)
21—30 of 31 matching pages
21: Bibliography W
…
►
Evaluating elliptic functions and their inverses.
Comput. Math. Appl. 39 (3-4), pp. 131–136.
…
►
Infinitely differentiable generalized logarithmic and exponential functions.
Math. Comp. 57 (196), pp. 723–733.
…
►
Reduction formulae for products of theta functions.
J. Res. Nat. Inst. Standards and Technology 117, pp. 297–303.
…
►
The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
…
►
The cubic transformation of the hypergeometric function.
Quart. J. Pure and Applied Math. 41, pp. 70–79.
…
22: Bibliography D
…
►
Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
.
Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
…
►
Computing Riemann theta functions.
Math. Comp. 73 (247), pp. 1417–1442.
…
►
Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
…
►
Theta functions and non-linear equations.
Uspekhi Mat. Nauk 36 (2(218)), pp. 11–80 (Russian).
…
►
Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
…
23: 9.9 Zeros
…
►
§9.9(ii) Relation to Modulus and Phase
… ►§9.9(iii) Derivatives With Respect to
… ►§9.9(iv) Asymptotic Expansions
… ►§9.9(v) Tables
►Tables 9.9.1 and 9.9.2 give 10D values of the first ten real zeros of , , , , together with the associated values of the derivative or the function. …24: 28.1 Special Notation
…
►(For other notation see Notation for the Special Functions.)
…
►The main functions treated in this chapter are the Mathieu functions
…and the modified Mathieu functions
…
►Alternative notations for the functions are as follows.
…
►
Abramowitz and Stegun (1964, Chapter 20)
…25: 3.4 Differentiation
…
►
§3.4(ii) Analytic Functions
… ►
3.4.19
►With the choice (which is crucial when is large because of numerical cancellation) the integrand equals at the dominant points , and in combination with the factor in front of the integral sign this gives a rough approximation to .
…
►
…
►
3.4.33
…
26: Bibliography I
…
►
Theta Functions.
Springer-Verlag, New York.
…
►
Computing zeros and orders of Bessel functions.
J. Comput. Appl. Math. 38 (1-3), pp. 169–184.
…
►
Tables of the elliptic cylinder functions.
Proc. Roy. Soc. Edinburgh Sect. A 52, pp. 355–433.
►
The periodic Lamé functions.
Proc. Roy. Soc. Edinburgh 60, pp. 47–63.
…
►
The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
…
27: 10.3 Graphics
§10.3 Graphics
►§10.3(i) Real Order and Variable
►For the modulus and phase functions , , , and see §10.18. … ►§10.3(ii) Real Order, Complex Variable
… ►§10.3(iii) Imaginary Order, Real Variable
…28: Errata
…
►
Subsection 19.11(i)
…
►
Equation (22.19.2)
►
Equation (22.19.3)
…
►
Chapters 8, 20, 36
…
►
References
…
A sentence and unnumbered equation
were added which indicate that care must be taken with the multivalued functions in (19.11.5). See (Cayley, 1961, pp. 103-106).
Suggested by Albert Groenenboom.
22.19.2
Originally the first argument to the function was given incorrectly as . The correct argument is .
Reported 2014-03-05 by Svante Janson.
22.19.3
Originally the first argument to the function was given incorrectly as . The correct argument is .
Reported 2014-03-05 by Svante Janson.
29: Bibliography K
…
►
Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
…
►
Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
…
►
Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
…
►
Theta relations and projective normality of Abelian varieties.
Amer. J. Math. 98 (4), pp. 865–889.
…
►
The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
…