Book Reviews: Atlas for computing mathematical functions

Thompson, William J.; Zachary, Joseph L.

doi:10.1063/1.168670

Cited by 27 publications

(42 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Their efficient numerical evaluation is a highly challenging task and typically one makes use of pre-compiled library routines [1]. In this study, we present a curious method which can design a one-dimensional (1D) quantum system in such a way that the resulting wavefunction is proportional to a given transcendental function taken from a certain class of functions.…”

Section: Introductionmentioning

confidence: 99%

The quantum Mellin transform

Twamley

Milburn

2006

New J. Phys.

View full text Add to dashboard Cite

The Berry--Keating operator on L2(R,dx) and on compact quantum graphs Sebastian Endres and Frank Steiner Abstract. We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to 'hyperbolic phase space' (η, p η ). We show that this new unitary change of basis from the position x on the half line to the hyperbolic momentum p η , transforms the wavefunction via a Mellin transform on to the critical line s = 1/2 − ip η . We utilize this new transform to find quantum wavefunctions whose hyperbolic momentum representation approximate a class of higher transcendental functions, and in particular, approximate the RiemannZeta function. We finally give possible physical realizations to perform an indirect measurement of the hyperbolic momentum of a quantum system on the half-line.

show abstract

Section: Introductionmentioning

confidence: 99%

The quantum Mellin transform

Twamley

Milburn

2006

New J. Phys.

View full text Add to dashboard Cite

show abstract

“…The south-east area is at the present time the most exploited and is the location of the largest wind farm-with a nominal potential of 20.10 MW of the seven islands that make up the Archipelago [21]. 9 Hourly mean wind speeds to one decimal place have been used. 10 Company belongs to the Board of Industry of the Autonomous Canarian Government.…”

Section: Article In Pressmentioning

confidence: 99%

Analysis of two-component mixture Weibull statistics for estimation of wind speed distributions

2007

View full text Add to dashboard Cite

“…The main special functions needed in rotational dynamics are the Jacobian elliptic functions and the incomplete and complete elliptic integrals (Bowman 1961;Byrd and Friedman 1971;Thompson 1997;Wolfram 2003). They are necessary in describing the analytical solution of the torque-free rotation of a general triaxial rigid body, the fundamental problem in rotational dynamics.…”

Section: Introductionmentioning

confidence: 99%

Fast computation of Jacobian elliptic functions and incomplete elliptic integrals for constant values of elliptic parameter and elliptic characteristic

Fukushima

2008

Celest Mech Dyn Astr

View full text Add to dashboard Cite

In order to accelerate the numerical evaluation of torque-free rotation of triaxial rigid bodies, we present a fast method to compute various kinds of elliptic functions for a series of the elliptic argument when the elliptic parameter and the elliptic characteristic are fixed. The functions we evaluate are the Jacobian elliptic functions and the incomplete elliptic integral of the second and third kinds regarded as a function of that of the first kind. The key technique is the utilization of the Maclaurin series expansion and the addition theorems with respect to the elliptic argument. The new method is around 25 times faster than the method using the incomplete elliptic integral of general kind and around 70 times faster than the method using mathematical libraries given in the latest version of Numerical Recipes.

show abstract

Book Reviews: Atlas for computing mathematical functions

Cited by 27 publications

References 0 publications

The quantum Mellin transform

The quantum Mellin transform

Analysis of two-component mixture Weibull statistics for estimation of wind speed distributions

Fast computation of Jacobian elliptic functions and incomplete elliptic integrals for constant values of elliptic parameter and elliptic characteristic

Contact Info

Product

Resources

About