Grid is a free and open-source Python library for constructing numerical grids to integrate, interpolate, and differentiate functions (e.g., molecular properties), with a strong emphasis on facilitating these operations in computational chemistry and conceptual density functional theory. Although designed, maintained, and released as a stand-alone Python library, Grid was originally developed for molecular integration, interpolation, and solving the Poisson equation in the HORTON and ChemTools packages. Grid is designed to be easy to use, extend, and maintain; this is why we use Python and adopt many principles of modern software development, including comprehensive documentation, extensive testing, continuous integration/delivery protocols, and package management. We leverage popular scientific packages, such as NumPy and SciPy, to ensure high efficiency and optimized performance in grid development. This article is the official release note of the Grid library showcasing its unique functionality and scope.

1.
S.
Lehtola
, “
A review on non-relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules
,”
Int. J. Quantum Chem.
119
,
e25968
(
2019
).
2.
G. S.
Ho
,
V. L.
Lignères
, and
E. A.
Carter
, “
Introducing profess: A new program for orbital-free density functional theory calculations
,”
Comput. Phys. Commun.
179
,
839
854
(
2008
).
3.
W.
Mi
,
X.
Shao
,
C.
Su
,
Y.
Zhou
,
S.
Zhang
,
Q.
Li
,
H.
Wang
,
L.
Zhang
,
M.
Miao
,
Y.
Wang
, and
Y.
Ma
, “
Atlas: A real-space finite-difference implementation of orbital-free density functional theory
,”
Comput. Phys. Commun.
200
,
87
95
(
2016
).
4.
A. D.
Becke
, “
Numerical Hartree-Fock-Slater calculations on diatomic molecules
,”
J. Chem. Phys.
76
,
6037
6045
(
1982
).
5.
A. D.
Becke
, “
Basis-set-free density-functional quantum chemistry
,”
Int. J. Quantum Chem.
36
,
599
609
(
1989
).
6.
A. D.
Becke
and
R. M.
Dickson
, “
Numerical solution of Schrödinger’s equation in polyatomic molecules
,”
J. Chem. Phys.
92
,
3610
3612
(
1990
).
7.
R. M.
Dickson
and
A. D.
Becke
, “
Basis-set-free local density-functional calculations of geometries of polyatomic molecules
,”
J. Chem. Phys.
99
,
3898
3905
(
1993
).
8.
F.
Heidar-Zadeh
,
M.
Richer
,
S.
Fias
,
R. A.
Miranda-Quintana
,
M.
Chan
,
M.
Franco-Perez
,
C. E.
Gonzalez-Espinoza
,
T. D.
Kim
,
C.
Lanssens
,
A. H. G.
Patel
,
X. D.
Yang
,
E.
Vohringer-Martinez
,
C.
Cardenas
,
T.
Verstraelen
, and
P. W.
Ayers
, “
An explicit approach to conceptual density functional theory descriptors of arbitrary order
,”
Chem. Phys. Lett.
660
,
307
312
(
2016
).
9.
T.
Lu
and
F.
Chen
, “
Multiwfn: A multifunctional wavefunction analyzer
,”
J. Comput. Chem.
33
,
580
592
(
2012
).
10.
A.
Otero-de-la-Roza
,
E. R.
Johnson
, and
V.
Luaña
, “
Critic2: A program for real-space analysis of quantum chemical interactions in solids
,”
Comput. Phys. Commun.
185
,
1007
1018
(
2014
).
11.
A.
Otero-de-la-Roza
,
M. A.
Blanco
,
A. M.
Pendás
, and
V.
Luaña
, “
Critic: A new program for the topological analysis of solid-state electron densities
,”
Comput. Phys. Commun.
180
,
157
166
(
2009
).
12.
P. W.
Ayers
,
S.
Fias
, and
F.
Heidar-Zadeh
, “
The axiomatic approach to chemical concepts
,”
Computat. Theor. Chem.
1142
,
83
87
(
2018
).
13.
J.
Andres
,
P. W.
Ayers
,
R. A.
Boto
,
R.
Carbo-Dorca
,
H.
Chermette
,
J.
Cioslowski
,
J.
Contreras-Garcia
,
D. L.
Cooper
,
G.
Frenking
,
C.
Gatti
,
F.
Heidar-Zadeh
,
L.
Joubert
,
Á.
Martín Pendás
,
E.
Matito
,
I.
Mayer
,
A. J.
Misquitta
,
Y. R.
Mo
,
J.
Pilme
,
P. L. A.
Popelier
,
M.
Rahm
,
E.
RamosCordoba
,
P.
Salvador
,
W. H. E.
Schwarz
,
S.
Shahbazian
,
B.
Silvi
,
M.
Sola
,
K.
Szalewicz
,
V.
Tognetti
,
F.
Weinhold
, and
E. L.
Zins
, “
Nine questions on energy decomposition analysis
,”
J. Comput. Chem.
40
,
2248
2283
(
2019
).
14.
Á.
Martín Pendás
,
E.
Francisco
,
D.
Suárez
,
A.
Costales
,
N.
Díaz
,
J.
Munárriz
,
T.
Rocha-Rinza
, and
J. M.
Guevara-Vela
, “
Atoms in molecules in real space: A fertile field for chemical bonding
,”
Phys. Chem. Chem. Phys.
25
,
10231
10262
(
2023
).
15.
R. F. W.
Bader
,
Atoms in Molecules: A Quantum Theory
(
Clarendon
,
Oxford
,
1990
).
16.
F. H.
Zadeh
and
S.
Shahbazian
, “
Toward a fuzzy atom view within the context of the quantum theory of atoms in molecules: Quasi-atoms
,”
Theor. Chem. Acc.
128
,
175
181
(
2011
).
17.
E.
Sanville
,
S. D.
Kenny
,
R.
Smith
, and
G.
Henkelman
, “
Improved grid-based algorithm for bader charge allocation
,”
J. Comput. Chem.
28
,
899
908
(
2007
).
18.
G.
Henkelman
,
A.
Arnaldsson
, and
H.
Jónsson
, “
A fast and robust algorithm for bader decomposition of charge density
,”
Comput. Mater. Sci.
36
,
354
360
(
2006
).
19.
J. I.
Rodriguez
,
A. M.
Koster
,
P. W.
Ayers
,
A.
Santos-Valle
,
A.
Vela
, and
G.
Merino
, “
An efficient grid-based scheme to compute QTAIM atomic properties without explicit calculation of zero-flux surfaces
,”
J. Comput. Chem.
30
,
1082
1092
(
2009
).
20.
J. I.
Rodriguez
,
R. F. W.
Bader
,
P. W.
Ayers
,
C.
Michel
,
A. W.
Gotz
, and
C.
Bo
, “
A high performance grid-based algorithm for computing QTAIM properties
,”
Chem. Phys. Lett.
472
,
149
152
(
2009
).
21.
M.
Yu
and
D. R.
Trinkle
, “
Accurate and efficient algorithm for Bader charge integration
,”
J. Chem. Phys.
134
,
064111
(
2011
).
22.
T.
Keith
, AIMALL (version 19.10. 12), Todd A. Keith, TK Gristmill Software: Overland park, KS (2019) URL: http://aim.tkgristmill.com.
23.
P. L.
Popelier
, “
MORPHY, a program for an automated “atoms in molecules” analysis
,”
Comput. Phys. Commun.
93
,
212
240
(
1996
).
24.
P. A.
Johnson
,
L. J.
Bartolotti
,
P. W.
Ayers
,
T.
Fievez
, and
P.
Geerlings
, “
Charge density and chemical reactivity: A unified view from conceptual DFT
,” in
Modern Charge Density Analysis
, edited by
C.
Gatti
and
P.
Macchi
(
Springer
,
New York
,
2012
), pp.
715
764
.
25.
V.
Tognetti
,
C.
Morell
, and
L.
Joubert
, “
Quantifying electro/nucleophilicity by partitioning the dual descriptor
,”
J. Comput. Chem.
36
,
649
659
(
2015
).
26.
P.
Geerlings
,
E.
Chamorro
,
P. K.
Chattaraj
,
F.
De Proft
,
J. L.
Gázquez
,
S.
Liu
,
C.
Morell
,
A.
Toro-Labbé
,
A.
Vela
, and
P.
Ayers
, “
Conceptual density functional theory: Status, prospects, issues
,”
Theor. Chem. Acc.
139
,
36
(
2020
).
27.
J. L.
Géazquez
and
M.
Franco-Péerez
, “
Finite temperature conceptual density functional theory
,”
Conceptual Density Functional Theory
(
John Wiley & Sons, Ltd.
,
2022
), Chap. 8, pp.
137
160
.
28.
F.
De Proft
,
P.
Geerlings
,
F.
Heidar-Zadeh
, and
P. W.
Ayers
, “
Conceptual density functional theory
,” in
Comprehensive Computational Chemistry
, 1st ed., edited by
M.
Yanez
and
R. J.
Boyd
(
Elsevier
,
Oxford
,
2024
), pp.
306
321
.
29.
A.
Robles
,
M.
Franco-Pérez
,
J. L.
Gázquez
,
C.
Cárdenas
, and
P.
Fuentealba
, “
Local electrophilicity
,”
J. Mol. Model.
24
,
245
(
2018
).
30.
J. L.
Gázquez
,
M.
Franco-Pérez
,
P. W.
Ayers
, and
A.
Vela
, “
Temperature-dependent approach to chemical reactivity concepts in density functional theory
,”
Int. J. Quantum Chem.
119
,
e25797
(
2019
).
31.
X.
He
,
M.
Li
,
C.
Rong
,
D.
Zhao
,
W.
Liu
,
P. W.
Ayers
, and
S.
Liu
, “
Some recent advances in density-based reactivity theory
,”
J. Phys. Chem. A
128
,
1183
1196
(
2024
).
32.
F. L.
Hirshfeld
, “
Bonded-atom fragments for describing molecular charge densities
,”
Theor. Chim. Acta
44
,
129
138
(
1977
).
33.
R. G.
Parr
,
P. W.
Ayers
, and
R. F.
Nalewajski
, “
What is an atom in a molecule?
,”
J. Phys. Chem. A
109
,
3957
3959
(
2005
).
34.
T.
Verstraelen
,
S.
Vandenbrande
,
F.
Heidar-Zadeh
,
L.
Vanduyfhuys
,
V.
Van Speybroeck
,
M.
Waroquier
, and
P. W.
Ayers
, “
Minimal basis iterative stockholder: Atoms in molecules for force-field development
,”
J. Chem. Theory Comput.
12
,
3894
3912
(
2016
).
35.
F.
Heidar-Zadeh
,
P. W.
Ayers
,
T.
Verstraelen
,
I.
Vinogradov
,
E.
Vöhringer-Martinez
, and
P.
Bultinck
, “
Information-theoretic approaches to atoms-in-molecules: Hirshfeld family of partitioning schemes
,”
J. Phys. Chem. A
122
,
4219
4245
(
2018
).
36.
R.
Bast
(
2021
). “
Numgrid: Numerical integration grid for molecules
,” Zenodo. https://doi.org/10.5281/zenodo.1470276
37.
Q.
Sun
,
T. C.
Berkelbach
,
N. S.
Blunt
,
G. H.
Booth
,
S.
Guo
,
Z.
Li
,
J.
Liu
,
J. D.
McClain
,
E. R.
Sayfutyarova
,
S.
Sharma
,
S.
Wouters
, and
G. K.-L.
Chan
, “
PySCF: The python-based simulations of chemistry framework
,”
WIREs Comput. Mol. Sci.
8
,
e1340
(
2018
).
38.
R. M.
Parrish
,
L. A.
Burns
,
D. G. A.
Smith
,
A. C.
Simmonett
,
A. E.
DePrince
,
E. G.
Hohenstein
,
U.
Bozkaya
,
A. Y.
Sokolov
,
R.
Di Remigio
,
R. M.
Richard
,
J. F.
Gonthier
,
A. M.
James
,
H. R.
McAlexander
,
A.
Kumar
,
M.
Saitow
,
X.
Wang
,
B. P.
Pritchard
,
P.
Verma
,
H. F.
Schaefer
,
K.
Patkowski
,
R. A.
King
,
E. F.
Valeev
,
F. A.
Evangelista
,
J. M.
Turney
,
T. D.
Crawford
, and
C. D.
Sherrill
, “
Psi4 1.1: An open-source electronic structure program emphasizing automation, advanced libraries, and interoperability
,”
J. Chem. Theory Comput.
13
,
3185
3197
(
2017
).
39.
L.
Lemmens
,
X.
De Vriendt
,
D.
Van Hende
,
T.
Huysentruyt
,
P.
Bultinck
, and
G.
Acke
, “
GQCP: The Ghent quantum chemistry package
,”
J. Chem. Phys.
155
,
084802
(
2021
).
40.
R.
Muller
,
PyQuante: Python quantum chemistry, URL:
http://pyquante.sourceforge.net (
2017
).
41.
J.
Lehtola
,
M.
Hakala
,
A.
Sakko
, and
K.
Hämäläinen
, “
ERKALE – A flexible program package for x-ray properties of atoms and molecules
,”
J. Comput. Chem.
33
,
1572
1585
(
2012
).
42.
J. P.
Unsleber
,
T.
Dresselhaus
,
K.
Klahr
,
D.
Schnieders
,
M.
Böckers
,
D.
Barton
, and
J.
Neugebauer
, “
Serenity: A subsystem quantum chemistry program
,”
J. Comput. Chem.
39
,
788
798
(
2018
).
43.
S. G.
Johnson
,
Multi-dimensional adaptive integration in C: The Cubature package
, https://github.com/stevengj/cubature (
2005
).
44.
A. D.
Becke
, “
A multicenter numerical integration scheme for polyatomic molecules
,”
J. Chem. Phys.
88
,
2547
2553
(
1988
).
45.
V. I.
Lebedev
and
D. N.
Laikov
, “
A quadrature formula for the sphere of the 131st algebraic order of accuracy
,”
Dokl. Math.
59
,
477
481
(
1999
) https://api.semanticscholar.org/CorpusID:118893131.
46.
M.
Chan
,
T.
Verstraelen
,
A.
Tehrani
,
M.
Richer
,
X.
Yang
,
T.
Kim
,
E.
Vöohringer-Martinez
,
F.
Heidar-Zadeh
, and
P. W.
Ayers
, “
The tale of HORTON: Lessons learned in a decade of scientific software development
,”
J. Chem. Phys
160
,
162501
(
2024
).
47.
L.
Pujal
,
A.
Tehrani
, and
F.
Heidar-Zadeh
, “
Chemtools: Gain chemical insight form quantum chemistry calculations
,” in
Conceptual Density Functional Theory: Towards a New Chemical Reactivity Theory
, 1st ed., edited by
S.
Liu
(
Wiley
,
2022
).
48.
T.
Verstraelen
,
W.
Adams
,
L.
Pujal
,
A.
Tehrani
,
B. D.
Kelly
,
L.
Macaya
,
F.
Meng
,
M.
Richer
,
R.
Hernández-Esparza
,
X. D.
Yang
,
M.
Chan
,
T. D.
Kim
,
M.
Cools-Ceuppens
,
V.
Chuiko
,
E.
Vöhringer-Martinez
,
P. W.
Ayers
, and
F.
Heidar-Zadeh
, “
IOData: A python library for reading, writing, and converting computational chemistry file formats and generating input files
,”
J. Comput. Chem.
42
,
458
464
(
2021
).
49.
T. D.
Kim
,
M.
Richer
,
G.
Sánchez-Díaz
,
R. A.
Miranda-Quintana
,
T.
Verstraelen
,
F.
Heidar-Zadeh
, and
P. W.
Ayers
, “
Fanpy: A python library for prototyping multideterminant methods in ab initio quantum chemistry
,”
J. Comput. Chem.
44
,
697
709
(
2023
).
50.
T. D.
Kim
,
R. A.
Miranda-Quintana
,
M.
Richer
, and
P. W.
Ayers
, “
Flexible ansatz for N-body configuration interaction
,”
Computat. Theor. Chem.
1202
,
113187
(
2021
).
51.
A.
Tehrani
,
J. S. M.
Anderson
,
D.
Chakraborty
,
J. I.
Rodriguez-Hernandez
,
D. C.
Thompson
,
T.
Verstraelen
,
P. W.
Ayers
, and
F.
Heidar-Zadeh
, “
An information-theoretic approach to basis-set fitting of electron densities and other non-negative functions
,”
J. Comput. Chem.
44
,
1998
2015
(
2023
).
52.
F.
Meng
,
M.
Richer
,
A.
Tehrani
,
J.
La
,
T. D.
Kim
,
P. W.
Ayers
, and
F.
Heidar-Zadeh
, “
Procrustes: A python library to find transformations that maximize the similarity between matrices
,”
Comput. Phys. Commun.
276
,
108334
(
2022
).
53.
B. D.
Lee
, “
Ten simple rules for documenting scientific software
, “
PLoS Comput. Biol.
14
,
e1006561
(
2018
).
54.
C. R.
Harris
,
K. J.
Millman
,
S. J.
van der Walt
,
R.
Gommers
,
P.
Virtanen
,
D.
Cournapeau
,
E.
Wieser
,
J.
Taylor
,
S.
Berg
,
N. J.
Smith
,
R.
Kern
,
M.
Picus
,
S.
Hoyer
,
M. H.
van Kerkwijk
,
M.
Brett
,
A.
Haldane
,
J. F.
del Río
,
M.
Wiebe
,
P.
Peterson
,
P.
Gérard-Marchant
,
K.
Sheppard
,
T.
Reddy
,
W.
Weckesser
,
H.
Abbasi
,
C.
Gohlke
, and
T. E.
Oliphant
, “
Array programming with NumPy
,”
Nature
585
,
357
362
(
2020
).
55.
P.
Virtanen
,
R.
Gommers
,
T. E.
Oliphant
,
M.
Haberland
,
T.
Reddy
,
D.
Cournapeau
,
E.
Burovski
,
P.
Peterson
,
W.
Weckesser
,
J.
Bright
,
S. J.
van der Walt
,
M.
Brett
,
J.
Wilson
,
K. J.
Millman
,
N.
Mayorov
,
A. R. J.
Nelson
,
E.
Jones
,
R.
Kern
,
E.
Larson
,
C. J.
Carey
,
İ.
Polat
,
Y.
Feng
,
E. W.
Moore
,
J.
VanderPlas
,
D.
Laxalde
,
J.
Perktold
,
R.
Cimrman
,
I.
Henriksen
,
E. A.
Quintero
,
C. R.
Harris
,
A. M.
Archibald
,
A. H.
Ribeiro
,
F.
Pedregosa
,
P.
van Mulbregt
, and
SciPy 1.0 Contributors
, “
SciPy 1.0: Fundamental algorithms for scientific computing in Python
,”
Nat. Methods
17
,
261
272
(
2020
).
56.
A.
Meurer
,
C. P.
Smith
,
M.
Paprocki
,
O.
Čertík
,
S. B.
Kirpichev
,
M.
Rocklin
,
A.
Kumar
,
S.
Ivanov
,
J. K.
Moore
,
S.
Singh
,
T.
Rathnayake
,
S.
Vig
,
B. E.
Granger
,
R. P.
Muller
,
F.
Bonazzi
,
H.
Gupta
,
S.
Vats
,
F.
Johansson
,
F.
Pedregosa
,
M. J.
Curry
,
A. R.
Terrel
,
Š.
Roučka
,
A.
Saboo
,
I.
Fernando
,
S.
Kulal
,
R.
Cimrman
, and
A.
Scopatz
, “
SymPy: Symbolic computing in python
,”
PeerJ Comput. Sci.
3
,
e103
(
2017
).
57.
R. F.
Stewart
,
E. R.
Davidson
, and
W. T.
Simpson
, “
Coherent X-ray scattering for the hydrogen atom in the hydrogen molecule
,”
J. Chem. Phys.
42
,
3175
3187
(
1965
).
58.
J.
Harris
, “
Simplified method for calculating the energy of weakly interacting fragments
,”
Phys. Rev. B
31
,
1770
1779
(
1985
).
59.
B.
Delley
, “
An all-electron numerical method for solving the local density functional for polyatomic molecules
,”
J. Chem. Phys.
92
,
508
517
(
1990
).
60.
B.
Delley
, “
From molecules to solids with the DMol3 approach
,”
J. Chem. Phys.
113
,
7756
7764
(
2000
).
61.
M.
Abramowitz
,
I. A.
Stegun
, and
R. H.
Romer
, “
Handbook of mathematical functions with formulas, graphs, and mathematical tables
,”
Am. J. Phys.
56
,
958
(
1988
).
62.
M.
Abramowitz
and
I.
Stegun
, “
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
,” (
1972
).
63.
H.
Takahasi
and
M.
Mori
, “
Double exponential formulas for numerical integration
,”
Publ. Res. Inst. Math. Sci.
9
,
721
741
(
1973
).
64.
N.
Hale
and
L. N.
Trefethen
, “
New quadrature formulas from conformal maps
,”
SIAM J. Numer. Anal.
46
,
930
948
(
2008
).
65.
V. I.
Lebedev
, “
Values of the nodes and weights of ninth to seventeenth order Gauss-Markov quadrature formulae invariant under the octahedron group with inversion
,”
USSR Comput. Math. Math. Phys.
15
,
44
51
(
1975
).
66.
V. I.
Lebedev
, “
Quadratures on a sphere
,”
USSR Comput. Math. Math. Phys.
16
,
10
24
(
1976
).
67.
V. I.
Lebedev
, “
Spherical quadrature formulas exact to orders 25–29
,”
Sib. Math. J.
18
,
99
107
(
1977
).
68.
V. I.
Lebedev
and
A. L.
Skorokhodov
, “
Quadrature formulas of orders 41, 47, and 53 for the sphere
,”
Dokl. Math.
45
,
587
592
(
1992
).
69.
V. I.
Lebedev
, “
A quadrature formula for a sphere that is the 59th algebraic order of accuracy
,”
Doklady Akademii Nauk
338
,
454
456
(
1994
).
70.
R. S.
Womersley
, “
Efficient spherical designs with good geometric properties
,”
Contemporary computational mathematics-A celebration of the 80th birthday of Ian Sloan
(
2018
), pp.
1243
1285
.
71.
C. H.
Beentjes
, “
Quadrature on a spherical surface
,” Working note available on the website http://people.maths.ox.ac.uk/beentjes/Essays (
2015
).
72.
S.-H.
Chien
and
P. M. W.
Gill
, “
SG-0: A small standard grid for dft quadrature on large systems
,”
J. Comput. Chem.
27
,
730
739
(
2006
).
73.
P. M.
Gill
,
B. G.
Johnson
, and
J. A.
Pople
, “
A standard grid for density functional calculations
,”
Chem. Phys. Lett.
209
,
506
512
(
1993
).
74.
S.
Dasgupta
and
J. M.
Herbert
, “
Standard grids for high-precision integration of modern density functionals: SG-2 and SG-3
,”
J. Comput. Chem.
38
,
869
882
(
2017
).
75.
H.
Laqua
,
J.
Kussmann
, and
C.
Ochsenfeld
, “
An improved molecular partitioning scheme for numerical quadratures in density functional theory
,”
J. Chem. Phys.
149
,
204111
(
2018
).
76.
R. F.
Stewart
, “
Electron population analysis with rigid pseudoatoms
,”
Acta Crystallogr., Sect. A
32
,
565
574
(
1976
).
77.
C.
De Boor
and
C.
De Boor
,
A Practical Guide to Splines
(
Springer-Verlag
,
New York
,
1978
), Vol.
27
.
78.
A. D.
Becke
and
R. M.
Dickson
, “
Numerical solution of Poisson’s equation in polyatomic molecules
,”
J. Chem. Phys.
89
,
2993
2997
(
1988
).
79.
P.
L’Ecuyer
, “
Non-uniform random variate generations
,”
International Encyclopedia of Statistical Science
(
Springer
,
2011
), p.
991
.
80.
J. M.
Perez-Jorda
, “
Electronic distribution, position probability density and ‘clouds of points’
,”
Eur. J. Phys.
10
,
224
(
1989
).
81.
D. C.
Thompson
and
P. W.
Ayers
, “
Thinking inside the box: Novel linear scaling algorithm for Coulomb potential evaluation
,”
Int. J. Quantum Chem.
106
,
787
794
(
2006
).
82.
J. I.
Rodriguez
,
D. C.
Thompson
,
J. S.
Anderson
,
J. W.
Thomson
, and
P. W.
Ayers
, “
A physically motivated sparse cubature scheme with applications to molecular density-functional theory
,”
J. Phys. A: Math. Theor.
41
,
365202
(
2008
).
83.
O. L.
Colombo
,
Numerical Methods for Harmonic Analysis on the Sphere (Department of Geodetic Science
(
The Ohio State University
,
1981
).
84.
S. A.
Holmes
and
W. E.
Featherstone
, “
A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalised associated legendre functions
,”
J. Geod.
76
,
279
299
(
2002
).
You do not currently have access to this content.