Handbook of Elliptic Integrals for Engineers and Physicists

By P. F. Byrd, M. Friedman. 2014

1,292 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f3b08f5d9b2385356673f5f63e7d7a84a6fc67ad

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. C. Vafa
2. Vladimir Kazakov
3. Sergei Gukov
4. David A. Singer
5. Aimei Zhang
6. R. Dijkgraaf
7. Guimin Chen
8. Marcos Mariño

In Computational Theory and Mathematics

1. C. Vafa
2. Y. Chu
3. Vladimir Kazakov
4. Horst Alzer
5. Sergei Gukov
6. David A. Singer
7. R. Dijkgraaf

In Numerical Analysis

1. C. Vafa
2. Y. Chu
3. Vladimir Kazakov
4. Sergei Gukov
5. David A. Singer
6. R. Dijkgraaf

Citations in the corpus

• Lectures on Elastic Curves and Rods (2008, background): “(See [ 6 ] for exhaustive details.) The complete elliptic integrals E(p) and K(p) are given by:”
• Estimating body mass of free‐living whales using aerial photogrammetry and 3D volumetrics (2019, methodology): “…et al. (1969), using the complete elliptic integral of the second kind formula to calculate the circumference (i.e. body girth, G ) of an ellipse (Byrd & Friedman, 2013): where r W represent the radius of the body width ( W ) and r H represent the radius of the body height ( H ) of whale i at…”
• Wireless Power Transfer in Loosely Coupled Links: Coil Misalignment Model (2011, background): “A solution for an integral of this form, which can be recognized asastandardellipticintegral,isdescribedbyGood[44]andalso in the extensive collection of elliptic integrals and special functions compiled by Byrd and Friedman in [ 45 ].”
• Monotonicity theorems and inequalities for the complete elliptic integrals (2004, background): “These and other representations for K and E can be found in the monographs [13,21], which also contain interesting historical remarks on elliptic integrals.”
• A Power Mean Inequality involving the complete elliptic integrals (2013, background): “The wellknown complete elliptic integrals of the first and second kind [9, 11] are respectively defined by”
• Perturbative analysis of gauged matrix models (2002, positive): “The function G(x), having the large x asymptotics G(x → ∞) = O(1/x(2)), can be represented as λ G(x) = x(2) − 1 4 − √ (x2 − a2)(x2 − b2) The function G(x), having the large x asymptotics G(x → ∞) = O(1/x(2)), can be represented as λ G(x) = x(2) − 1 4 − √ (x2 − a2)(x2 − b2) The large x asymptotics fi”
• A Comprehensive Elliptic Integral Solution to the Large Deflection Problems of Thin Beams in Compliant Mechanisms (2012, background): “The incomplete elliptic integrals of the first and second kinds are defined as [22]”
• Chebyshev property of complete elliptic integrals and its application to abelian integrals (2002, neutral): “05 of [2] , O2i satisfy the following recurrence formula: O2i+2 = 2i(1 + k(2))O2i + (1 − 2i)O2i−2 (2i + 1)k2 ,”