• Corpus ID: 7670832

Digital Library of Mathematical Functions

  title={Digital Library of Mathematical Functions},
  author={Daniel W. Lozier and Ronald F. Boisvert and Joyce Conlon and Marjorie A. McClain and Bruce R. Fabijonas and Raghu N Kacker and Bruce L. Miller and Frank W. J. Olver and Bonita V. Saunders and Abdou Youssef and Charles W. Clark},
Daniel Lozier Ronald Boisvert Joyce Conlon Marjorie McClain Bruce Fabijonas Raghu Kacker Bruce Miller F.W.J. Olver Bonita Saunders Abdou Youssef Charles Clark (NIST PL) Gloria Wiersma (NIST PL) Charles Hagwood (NIST ITL) Nell Sedransk (NIST ITL) Qiming Wang (NIST ITL) Shauntia Burley (Student) Michael Huber (Student) Elaine Kim (Student) Richard Askey (U. of Wisconsin, Madison) Michael Berry (U. Bristol, UK) Leonard Maximon (George Washington) Morris Newman (U. California, Santa Barbara) Ingram… 
A novel approach to the Lindel\"of hypothesis.
Lindel{o}f's hypothesis, one of the most important open problems in the history of mathematics, states that for large $t$, Riemann's zeta function $\zeta(1/2+it)$ is of order $O(t^{\varepsilon})$ for
Arbitrary-precision computation of the gamma function
The best methods available for computing the gamma function Γ(z) in arbitrary-precision arithmetic with rigorous error bounds are discussed and some new formulas, estimates, bounds and algorithmic improvements are presented.
Computing Riemann theta functions in Sage with applications
A new implementation for the computation of the Riemann theta function in the open-source mathematical software Sage is discussed, and is the first step towards porting the functionality of the algcurves package to Sage as well as other scientific Python distributions.
Second order expansion for the nonlocal perimeter functional
The seminal results of Bourgain, Brezis, Mironescu [8] and Dávila [18] show that the classical perimeter can be approximated by a family of nonlocal perimeter functionals. We consider a corresponding
A Relativistic Conical Function and its Whittaker Limits
In previous work we introduced and studied a function R(a+;a ;c;v; ^) that is a generalization of the hypergeometric function 2F1 and the Askey{Wilson polynomials. When the coupling vector c 2 C 4 is
Central factorials under the Kontorovich–Lebedev transform of polynomials
In this paper, we show that slight modifications of the Kontorovich–Lebedev (KL) transform lead to an automorphism of the vector space of polynomials. This circumstance along with the Mellin
Construction and implementation of asymptotic expansions for Laguerre-type orthogonal polynomials
This work extends the case of Jacobi and Jacobi-type polynomials and supply an implementation with explicit expansions in four different regions of the complex plane that may be used to compute Gauss-Laguerre quadrature rules in a lower computational complexity than based on the recurrence relation, and with improved accuracy for large degree.
Acceleration of generalized hypergeometric functions through precise remainder asymptotics
A new series acceleration technique is derived that can be applied to any hypergeometric function, even with complex parameters and at the branch point z = 1.
On lattice sums and Wigner limits
Wigner limits are given formally as the difference between a lattice sum, associated to a positive definite quadratic form, and a corresponding multiple integral. To define these limits, which arose
MPFUN2015: A Thread-Safe Arbitrary Precision Computation Package (Full Documentation)
A new package that is 100% thread-safe, even at the language interface level, by means of data structures and algorithmic techniques that avoid the need to generate \context" (except for exceedingly high precision), yet still permit the working precision level to be dynamically changed during execution.


Asymptotically optimal quantum circuits for d-level systems.
Both a lower bound and a constructive upper bound on the number of two-qudit gates result, proving a sharp asymptotic of theta(d(2n)) gates, which closes the complexity question for all d-level systems (d finite).
Quantum computation with optical coherent states
We show that quantum computation circuits using coherent states as the logical qubits can be constructed from simple linear networks, conditional photon measurements, and "small" coherent
Automatic Synthesis and Simulation of Quantum Circuits
  • Automatic Synthesis and Simulation of Quantum Circuits
  • 2004
Control Theoretic Aspects of Holonomic Quantum Computation
  • Dennis Lucarelli (JHU APL) Match
  • 2004
JHU APL), Control Theoretic Aspects of Holonomic Quantum Computation, Match
  • 2004
Limits of Quantum Computation
  • Limits of Quantum Computation
  • 2004
Naval Research Lab), Pseudo-Random Operators for Quantum Information
  • Processing, September
  • 2004
Naval Research Lab), Pseudo-Random Operators for Quantum Information Processing
  • Naval Research Lab), Pseudo-Random Operators for Quantum Information Processing
  • 2004
Quantum Computation with Optical
  • Coherent States, October
  • 2004
Quantum Information Processing in lattices
  • Quantum Information Processing in lattices
  • 2004