Howard S. Cohl, Ph.D.
Applied and Computational Mathematics Division
National Institute for Standards and Technology
Mission Viejo, California, 92694, U.S.A.
email: howard.cohlatnist.gov
http://hcohl.sdf.org/
http://www.nist.gov/itl/math/msg/howardscohl.cfm
BIBLIOGRAPHY

Dynamic Instabilities in Rotating, LowMass Protostars during
Early Disk Formation,
with S. Yang, R. H. Durisen, J. N. Imamura and J. Toman,
Icarus, 91, 1428,
15 pages.
ABSTRACT
PDF
(1991)

The Solar White Light Flare of 1989 March 7: Simultaneous
Multiwavelength Observations at High Time Resolution, with
D. F. Neidig, A. L. Kiplinger and P. H. Wiborg,
The Astrophysical
Journal, 46, 306318, 13 pages.
ABSTRACT
PDF
(1993)

Parallel Implementation of a DataTranspose Technique
for the Solution of Poisson's Equation in Cylindrical Coordinates,
with XH Sun and J. E. Tohline,
Proceedings of the 8th SIAM Conference on Parallel Processing
for Scientific Computing, Minneapolis, Minnesota, March, 8 pages.
PDF
(1997)

The Formation of CommonEnvelope, PreMainSequence Binary Stars,
with J. E. Tohline, J. E. Cazes,
Proceedings of Numerical Astrophysics,
ed. T. Hanawa,
ABSTRACT
PDF
(1998)

On the numerical solution of the cylindrical
Poisson equation for isolated selfgravitating systems,
The Louisiana State University and Agricultural and Mechanical College, ix+122 pages.
ABSTRACT
PDF
(1999)

A Compact Cylindrical Green's Function
Expansion for the Solution of Potential Problems, with J. E. Tohline,
The Astrophysical Journal,
527, 1, 86101, 16 pages.
ABSTRACT
PDF
(1999)

Developments in determining the gravitational potential using
toroidal functions, with
J. E. Tohline, A. R. P. Rau and H. M. Srivastava (2000)
Astronomische Nachrichten, 321, 5/6,
363372, 10 pages.
ABSTRACT
PDF
(2000)

Useful alternative to the
multipole expansion of 1/r potentials,
with A. R. P. Rau, J. E. Tohline, D. A. Browne, J. E. Cazes,
and E. I. Barnes,
Physical
Review A: Atomic and Molecular Physics and Dynamics, 64, 5, 52509,
5 pages.
ABSTRACT
PDF
(2001)

Portent of Heine's Reciprocal Square Root Identity,
Proceedings of the 3D Stellar Evolution Workshop,
ed. R. Cavallo, S. Keller, S. Turcotte, Livermore, California, July, 6 pages.
PDF
(2002)

Discrete Fourier Inversion of Linear Inhomogeneity,
Proceeding of the Fifth International Conference of Symmetry in Nonlinear Mathematical Physics,
June 2329, 2003, Institute of Mathematics, National Academy of
Sciences of Ukraine, Kyiv (Kiev), Ukraine, 7 pages.
PDF
(2003)
 On the relative motions of dense cores and envelopes in
starforming molecular clouds, with
B. A. Ayliffe, J. C. Langdon, M. R. Bate, Monthly Notices of
the Royal Astronomical Society, 374, 4, 11981206, 9 pages.
ABSTRACT
PDF
(2007)

Exact Fourier expansion in cylindrical
coordinates for the threedimensional Helmholtz Green function,
with J. T. Conway,
Zeitschrift
angewandte für Mathematik und Physik,
61, 3, June 2010, 425443, 19 pages.
ABSTRACT
PDF
(2010)
erratum

Derivatives with respect to the degree and
order of associated Legendre functions for z>1 using modified
Bessel functions,
Integral
Transforms and Special Functions,
21, 8, August 2010, 581588, 8 pages.
ABSTRACT
PDF
(2010)

Fourier and Gegenbauer expansions for fundamental solutions
of the Laplacian and powers in R^{d} and
H^{d},
The University of Auckland, xiv+190 pages.
ABSTRACT
PDF
(2010)
erratum

Generalized Heine's identity for complex Fourier series of binomials,
with D. E. Dominici,
Proceedings of the Royal Society A,
467, February 2011, 333345, 13 pages.
ABSTRACT
PDF
(2011)
 On parameter differentiation for integral representations of associated
Legendre functions,
Symmetry, Integrability
and Geometry: Methods and Applications (SIGMA),
Special Issue on Symmetry, Separation, Superintegrability and Special
Functions (S^{4}),
7, 050, 16 pages.
ABSTRACT
PDF
(2011)
 Opposite Antipodal Fundamental Solution of Laplace's Equation in Hyperspherical Geometry,
Symmetry, Integrability and Geometry:
Methods and Applications (SIGMA),
7, 108, 14 pages.
ABSTRACT
PDF
(2011)

Fourier and Gegenbauer expansions for fundamental solutions
of the Laplacian in the hyperboloid model of hyperbolic geometry,
with E. G. Kalnins,
Journal of Physics A:
Mathematical and Theoretical, 45, 14, 145206, 32 pages.
ABSTRACT
PDF
(2012)
erratum
 Table errata to "Formulas and theorems for the special functions
of mathematical physics" by W. Magnus, F. Oberhettinger & R. P. Soni (1966),
Mathematics of Computation, 81, 280, 22512251, 1 page.
ABSTRACT
PDF (2012)
 Eigenfunction expansions for a
fundamental solution of Laplace's equation on R^{3} in parabolic and
elliptic cylinder coordinates, with H. Volkmer,
Journal of
Physics A: Mathematical and Theoretical,
45, 35, 355204, 20 pages.
ABSTRACT
PDF
(2012)
 Erratum: "Developments in determining the gravitational potential
using toroidal functions," Astronomische
Nachrichten,
333, 8, 784785, 2 pages.
ABSTRACT
PDF
(2012)
 Definite integrals using orthogonality and integral transforms,
with H. Volkmer,
Symmetry, Integrability and Geometry:
Methods and Applications (SIGMA),
Special Issue on Superintegrability, Exact Solvability, and Special
Functions,
8, 077, 10 pages.
ABSTRACT
PDF
(2012)
 Fourier, Gegenbauer and Jacobi expansions for
a powerlaw fundamental solution of the polyharmonic
equation and polyspherical addition theorems,
Symmetry, Integrability and Geometry:
Methods and Applications (SIGMA)
9, 042, 26 pages.
ABSTRACT
PDF
(2013)
erratum

Fourier expansions for a logarithmic fundamental solution of
the polyharmonic equation,
Journal of
Classical Analysis, 2, 2, 107127, 21 pages.
ABSTRACT
PDF
(2013)

Separation of variables in an asymmetric
cyclidic coordinate system, with H. Volkmer,
Journal of Mathematical Physics,
54, 6, 063513, 23 pages.
ABSTRACT
PDF
(2013)

Generalizations of generating functions for hypergeometric orthogonal
polynomials with definite integrals, with C. MacKenzie and H. Volkmer,
Journal of
Mathematical Analysis and Applications, 407, 2, 211225, 15 pages.
ABSTRACT
PDF
(2013)
erratum
 Publisher's Note: ``Separation of variables in an asymmetric
cyclidic coordinate system'' [J. Math. Phys. 54, 6, 063513 (2013)],
with H. Volkmer,
Journal of Mathematical Physics, 54,
7, 079904, 1 page.
ABSTRACT
PDF
(2013)

On a generalization of the generating function for
Gegenbauer polynomials,
Integral
Transforms and Special Functions, 24, 10, 807816, 10 pages.
ABSTRACT
PDF
(2013)
 Generalizations and specializations of generating functions
for Jacobi, Gegenbauer, Chebyshev and Legendre polynomials with
definite integrals, with C. MacKenzie,
Journal of
Classical Analysis, 3, 1, 1733, 17 pages.
ABSTRACT
PDF
(2013)
erratum

Digital Repository of Mathematical Formulae, with M. A. McClain,
B. V. Saunders, M. Schubotz and J. C. Williams,
Conferences on Intelligent
Computer Mathematics 2014, Coimbra, Portugal, July 711, 2014,
Lecture Notes in Artificial Intelligence 8543, Springer,
Eds. S. M. Watt, J. H. Davenport, A. P. Sexton, P. Sojka, J. Urban, 419422, 4 pages.
ABSTRACT
PDF (2014)

Expansions for a fundamental solution of Laplace's equation on
R^{3} in 5cyclidic harmonics, with H. Volkmer,
Analysis and Applications,
Special Issue: Dedicated to the Memory of Frank Olver, 12, 6, 613633, 21 pages.
ABSTRACT
PDF
(2014)

Evaluation of SimilarityMeausure Factors for Formulae bases on the NTCIR11 Math Task,
with M. Schubotz, A. Youssef, V. Markl and J. J. Li,
Proceedings of the 11th NTCIR Conference,
Tokyo, Japan, December 912, 2014,
ABSTRACT
PDF (2014)

Measurement and Analysis of the Lowest Resonant Mode of a Spherical
AnnularSector Patch Antenna, with S. J. Weiss and A. Boliong,
Institution of Engineering and Technology (IET) Microwaves, Antennas & Propagation, 9, 2, 95100, 6 pages.
ABSTRACT
PDF (2015)

Fourier and Gegenbauer expansions for a fundamental solution of
Laplace's equation in hyperspherical geometry,
with R. M. Palmer,
Symmetry, Integrability and Geometry:
Methods and Applications (SIGMA),
Special Issue on
Exact Solvability and
Symmetry Avatars in honour of Luc Vinet,
11, 015, 23 pages.
ABSTRACT
PDF
(2015)

Generalizations of generating functions for higher continuous
hypergeometric orthogonal polynomials in the Askey scheme,
with M. A. Baeder and H. Volkmer,
Journal of
Mathematical Analysis and Applications,
427, 1, 377398, 22 pages.
ABSTRACT
PDF
(2015)

Open problems at OPSFA12, Sousse, Tunisia, Edited by: Christian Berg, Sections authored by: Mohamed J. Atia, Howard Cohl,
Anbu Swaminathan and Walter Van Assche,
Integral
Transforms and Special Functions,
26, 2, 9095, 6 pages.
ABSTRACT
PDF
(2015)

UWB Signal Processing: Projection, BSplines and Modified Gegenbauer Bases, with Stephen D. Casey,
2015, Sampling Theory and Applications, 11th International Conference 2015,
American University, Washington DC, USA, May 2529.
ABSTRACT
PDF
(2015)

Growing the Digital Repository of Mathematical Formulae with Generic LaTeX Sources, with Moritz Schubotz,
Marje A. McClain, Bonita V. Saunders, Cherry Y. Zou,
Azeem S. Mohammed and Alex A. Danoff,
Conference on Intelligent Computer
Mathematics 2015, Washington DC, USA, July 1317, 2015,
Lecture Notes in Artificial Intelligence 9150, Springer,
Eds. M. Kerber, J. Carette, C. Kaliszyk, F. Rabe, V. Sorge, 280287, 8 pages.
ABSTRACT
PDF
(2015)

Challenges of Mathematical Information Retrieval in the NTCIR11 Math Wikipedia Task, with Moritz
Schubotz, Abdou Youssef and Volker Markl, The 38th Annual ACM Special Interest
Group on Information Retrieval Conference (SIGIR 2015), Santiago, Chile, August 913, 2015.
ABSTRACT
PDF
(2015)
 Report from the Open Problems session at OPSFA13, Edited by: Howard S. Cohl, Sections authored by:
Richard Askey, Ted Chihara, Howard S. Cohl, Charles F. Dunkl, Christoph Koutschan,
Sheehan Olver, Rick K. Beatson, Wolfgang zu Castell, Yuan Xu and Wadim Zudilin,
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA),
Special
Issue on Orthogonal Polynomials, Special Functions and
Applications, 12, 071, 12 pages.
ABSTRACT
PDF
(2016)
 Semantification of Identifiers in Mathematics for Better Math Information
Retrieval, with Moritz Schubotz, Alexey Grigorev, Marcus Leich,
Norman Meuschke, Bela Gipp, Abdou Youssef and Volker Markl,
The 39th Annual ACM Special Interest
Group on Information Retrieval Conference (SIGIR 2016), Pisa, Tuscany, Italy,
July 1721, 2016, 10 pages.
ABSTRACT
PDF
(2016)
 Getting the units right,
with Moritz Schubotz and David Veenhuis,
Work in Progress Section of DML
track for 9^{th}
Conference on Intelligent Computer Mathematics (CICM 2016), Bialystok, Poland, July 2529, 2016,
CEUR Workshop Proceedings, 1785, 11 pages.
ABSTRACT
PDF
(2016)

Convergence of Magnus integral addition theorems for confluent hypergeometric functions,
with Jessica E. Hirtenstein and Hans Volkmer,
Integral
Transforms and Special Functions, 27, 10, 767774, 8 pages.
ABSTRACT
PDF
(2016)

Some dual definite integrals for Bessel functions of the first kind,
with Sean J. Nair and Rebekah M. Palmer,
Scientia,
Series A : Mathematical Science, 27, 1530, 16 pages.
ABSTRACT
PDF
(2016)

Sampling Architectures for UltraWideband Signals, with Stephen D. Casey, 2017,
Sampling Theory and Applications,
12th International Conference 2017,
Tallinn, Estonia, July 37, 5 pages.
ABSTRACT
PDF
(2017)

Semantic Preserving Bijective Mappings of Mathematical Formulae between Word Processors
and Computer Algebra Systems,
Howard S. Cohl, Moritz Schubotz, Abdou Youssef, André
GreinerPetter, Jürgen Gerhard, Bonita V. Saunders, Marjorie A. McClain,
Joon Bang and Kevin Chen,
Conference on Intelligent Computer
Mathematics 2017, Edinburgh, Scotland, U.K., July 1721, 2017,
Lecture Notes in Computer Science 10383, Springer,
Eds. H. Geuvers, M. England, O. Hasan, F. Rabe, O. Teschke, 115131, 17 pages.
ABSTRACT
PDF
(2017)

VMEXT: A Visualization Tool for Mathematical Expression Trees,
Moritz Schubotz, Norman Meuschke, Thomas Hepp, Howard S. Cohl and Bela Gipp,
Conference on Intelligent Computer
Mathematics 2017, Edinburgh, Scotland, U.K., July 1721, 2017,
Lecture Notes in Computer Science 10383, Springer,
Eds. H. Geuvers, M. England, O. Hasan, F. Rabe, O. Teschke, 340355, 16 pages.
ABSTRACT
PDF
(2017)

Content dictionary description: select symbols from
Chapter 9 of the KLS dataset in the DRMF, Moritz Schubotz and
Howard S. Cohl, OpenMath Workshop in
Conference on Intelligent Computer
Mathematics 2017,
Edinburgh, Scotland, U.K., July 1721, 2017, 4 pages.
PDF
(2017)

The power collection method for connection relations: Meixner polynomials,
with Michael A. Baeder, Roberto S. CostasSantos and Wenqing Xu,
Journal of
Classical Analysis, 11, 2, 107128, 22 pages.
ABSTRACT
PDF
(2017)

The orthogonality of AlSalamCarlitz polynomials for complex parameters,
with Roberto S. CostasSantos and Wenqing Xu,
Frontiers in Orthogonal Polynomials and qSeries, Contemporary Mathematics and
its Applications: Monographs, Expositions and Lecture Notes, Vol. 1, World Scientific
Publishing Company, Cambridge, MA, Eds. Zuhair Nashed and Xin Li, Chapter 8,
155167, 13 pages.
ABSTRACT
PDF
(2018)

Improving the Representation and Conversion of Mathematical Formulae by Considering their
Textual Context, with Moritz Schubotz, André GreinerPetter, Philipp Scharpf,
Norman Meuschke, Bela Gipp, Proceedings of the Joint
Conference on Digital Libraries (JCDL'18), June 36, Fort Worth, Texas, USA,
doi 10.1145/3197026.3197058, 233242, 10 pages.
ABSTRACT
PDF
(2018)

Automated Symbolic and Numerical Testing of DLMF Formulae using Computer Algebra Systems,
with André GreinerPetter and Moritz Schubotz,
Conference on Intelligent Computer
Mathematics 2018, Hagenberg, Austria, August 1317, 2018,
Lecture Notes in Computer Science 11006, Springer,
Eds. F. Rabe, W. Farmer, G.O. Passmore, A. Youssef, 3952, 14 pages.
ABSTRACT
PDF
(2018)

MathTools: An Open API for Convenient MathML Handling,
with André GreinerPetter, Moritz Schubotz and Bela Gipp,
Conference on Intelligent Computer
Mathematics 2018, Hagenberg, Austria, August 1317, 2018,
Lecture Notes in Computer Science 11006, Springer,
Eds. F. Rabe, W. Farmer, G.O. Passmore, A. Youssef, 104110, 7 pages.
ABSTRACT
PDF
(2018)

Some generating functions for qpolynomials,
with Roberto S. CostasSantos and Tanay V. Wakhare,
Symmetry,
10, 12, 758, 12 pages.
ABSTRACT
PDF
(2018)
 Fundamental Solutions and Gegenbauer Expansions of Helmholtz Operators
in Riemannian Spaces of Constant Curvature, with Thinh H. Dang and T. M. Dunster,
Symmetry, Integrability and Geometry:
Methods and Applications (SIGMA),
Special Issue on Orthogonal Polynomials, Special Functions
and Applications (OPSFA14), 14, 136, 45 pages.
ABSTRACT
PDF
(2018)
 Improving the representation and conversion of mathematical formulae by
considering their textual context, reprint of https://doi.org/10.1145/3197026.3197058, with Moritz Schubotz André GreinerPetter,
Philipp Scharpf, Norman Meuschke, Bela Gipp,
TUGBOAT, The Communications
of the TeX Users Group,
39, 3, 228240, 13 pages.
ABSTRACT
PDF
(2018)

On a generalization of the Rogers generating function,
with Roberto S. CostasSantos and Tanay V. Wakhare,
Journal
of Mathematical Analysis and Applications,
475, 2, 10191043, 25 pages.
ABSTRACT
PDF
(2019)

Semantic Preserving Bijective Mappings for Expressions involving Special
Functions between Computer Algebra Systems and Document Preparation Systems,
with André GreinerPetter, Moritz Schubotz and Bela Gipp,
ASLIB Journal
of Information Management,
71, 3, 415439, 24 pages.
ABSTRACT
PDF
(2019)

Towards Formula Concept Discovery and Recognition,
with Philipp Scharpf, Moritz Schubotz and Bela Gipp,
Proceedings of the 4th Joint Workshop on Bibliometricenhanced Information
Retrieval and Natural Language Processing for Digital Libraries (BIRNDL) colocated with the
42nd International ACM SIGIR Conference, CEURWS, 2414, 108115, 8 pages.
ABSTRACT
PDF
(2019)

Discovering Mathematical Objects of Interest—A Study of Mathematical Notations,
with André GreinerPetter, Moritz Schubotz, Fabian Müller, Corrina Breitinger,
Akiko Aizawa and Bela Gipp,
WWW'20: Proceedings of
the Web Conference 2020,
ACM Digital Library, Eds. Y. Huang, I. King, T.Y. Liu, M. van Steen,
April 2020, 14451456, 12 pages.
ABSTRACT
PDF
(2020)

Terminating Basic Hypergeometric
Representations and Transformations for
the AskeyWilson Polynomials, with
Roberto S. CostasSantos and Linus Ge,
Symmetry,
12, 8, 1290, 14 pages.
ABSTRACT
PDF
(2020)

MultiIntegral Representations for Associated Legendre and Ferrers Functions,
with
Roberto S. CostasSantos,
Symmetry,
12, 10, 1598, 22 pages.
ABSTRACT
PDF
(2020)

Lectures on Orthogonal Polynomials and Special Functions,
OPSFA Sixth Summer School, Norbert Wiener Center, University of Maryland,
College Park, Maryland, July 1115, 2016. Edited by Howard S. Cohl and Mourad E. H. Ismail,
London Mathematical Society Lecture Note Series, 464,
Cambridge University Press, Cambridge,
ISBN: 9781108908993, xvi+334
DOI
(2020)

Correction: Cohl, H.S.; CostasSantos, R.S.; Ge, L. Terminating Basic
Hypergeometric Representations and Transformations for the AskeyWilson Polynomials,
Symmetry 2020, 12, 1290, with Roberto S. CostasSantos and Linus Ge,
Symmetry,
12, 12, 2120, 2 pages.
ABSTRACT
PDF
(2020)
 Gauss hypergeometric representations of the Ferrers function of the second kind,
with Justin Park and Hans Volkmer,
Symmetry, Integrability and Geometry:
Methods and Applications (SIGMA),
17, 053, 33 pages.
ABSTRACT
PDF
(2021)
 Connecting Islands: Bridging zbMATH and DLMF with Scholix. A blueprint for
connecting expert knowledge systems, with Moritz Schubotz and Olaf Teschke,
European
Mathematical Society (EMS) Magazine, 120, 6667, 2 pages.
ABSTRACT
PDF
(2021)

The Legacy of Dick Askey (19332019),
Edited by: Howard S. Cohl, Mourad E. H. Ismail and HungHsi Wu,
Sections authored by: Paul Terwilliger, George E. Andrews, Krishnaswami Alladi, Bruce C. Berndt, Luc Vinet, Alexei Zhedanov, Dennis Stanton, Mourad E. H. Ismail, George Gasper, Tom H. Koornwinder, HungHsi Wu, Al Cuoco and Roger Howe,
Notices
of the American Mathematical Society, January 2022, 69, 01, 5975, 17 pages.
ABSTRACT
PDF (2022)

Comparative Verification of the Digital Library of Mathematical Functions and Computer
Algebra Systems, with André GreinerPetter,
Abdou Youssef, Moritz Schubotz,
Avi Trost, Rajen Dey, Akiko Aizawa and Bela Gipp,
Tools and Algorithms for the Construction and
Analysis of Systems (TACAS 2022), Munich, Germany, April 27, 2022,
Held as Part of the European Joint Conferences on Theorey and Practice of Software, ETAPS 2022,
Lecture Notes in Computer Science 13243, Springer,
Eds. D. Fisman, G. Rosu, 87105, 19 pages.
ABSTRACT
PDF
(2022)

On the relation between Gegenbauer polynomials and the Ferrers function of the first kind,
with Roberto S. CostasSantos,
Analysis Mathematica,
48, 2,
arXiv:2108.03276
PDF
(2022)
 Expansion for a Fundamental Solution of Laplace's Equation in FlatRing Cyclide Coordinates,
with Lijuan Bi and Hans Volkmer,
Symmetry, Integrability and Geometry:
Methods and Applications (SIGMA),
18, 041, 31 pages.
ABSTRACT
PDF
(2022)

Utility of integral representations for basic hypergeometric functions and
orthogonal polynomials, with Roberto S. CostasSantos, to appear in
The Ramanujan Journal,
Special Volume Dedicated to Dick Askey,
arXiv:2108.03275
PDF
(2022)

Liber Amicorum, a Friendship Book for Dick Askey, Edited by: Howard S. Cohl, Mourad E. H. Ismail,
to appear in Celebratio Mathematica (2022)

The Digital Shadow of Mathematics and its Ramifications, with Moritz Schubotz,
to appear in
Jahrbuch über die Fortschritte der Mathematik (2022)

Generalizations of generating functions for basic hypergeometric orthogonal polynomials,
with Roberto S. CostasSantos, Philbert R. Hwang and Tanay V. Wakhare,
to appear in
Open Journal of Mathematical Sciences
arXiv:1411.1371 (2022)

Peanut harmonic expansion for a fundamental solution of Laplace's equation in flatring coordinates,
with Lijuan Bi and Hans Volkmer,
to appear in
Analysis Mathematica
arXiv:2202.08923 (2022)

Gegenbauer expansions and addition theorems for a binomial and logarithmic fundamental solution of the evendimensional Euclidean polyharmonic equation,
with Jessie E. Hirtenstein, Jim Lawrence and Lisa Ritter,
to appear in
Journal
of Mathematical Analysis and Applications
arXiv:2203.06134 (2022)

Symmetry of terminating series representations of the AskeyWilson polynomials,
with Roberto S. CostasSantos,
to appear in
Journal
of Mathematical Analysis and Applications
arXiv:2202.08911 (2022)

Nonterminating transformations and summations associated with some qMellinBarnes integrals,
with Roberto S. CostasSantos,
arXiv:2206.05222
(submitted). (2022)

Twodimensional contiguous relations for linearization coefficients of orthogonal polynomials in the Askeyscheme,
with Lisa Ritter,
arXiv:2206.05230
(submitted). (2022)

Discovery and Recognition of Formula Concepts using Machine Learning,
with Philipp Scharpf, Moritz Schubotz and Bela Gipp, (submitted). (2022)