- Bound-state and impedance calculations
- Max Born and Emil Wolf,
*Principles of Optics* - Eugen Merzbacher,
*Quantum Mechanics* - Leonard Schiff,
*Quantum Mechanics*

- Max Born and Emil Wolf,
- Calderón-Zygmund and wavelet theory
- Yves Meyer,
*Wavelets and Operators* - Ingrid Daubechies,
*Ten Lectures on Wavelets* - Stéphane Mallat,
*A Wavelet Tour of Signal Processing*

- Yves Meyer,
- Complex analysis
- Lars Ahlfors,
*Complex Analysis*

- Lars Ahlfors,
- Fourier analysis
- Harry Dym and Henry McKean,
*Fourier Series and Integrals* - Yitzhak Katznelson,
*An Introduction to Harmonic Analysis*

- Harry Dym and Henry McKean,
- Functional analysis
- Frigyes Riesz and Béla Sz.-Nagy,
*Functional Analysis* - Andrei Kolmogorov and Sergei Fomin,
*Introductory Real Analysis* - Peter Lax,
*Functional Analysis* - Walter Rudin,
*Functional Analysis*

- Frigyes Riesz and Béla Sz.-Nagy,
- Mathematical methods in physics
(including multipole/partial-wave expansions)
- Philip Morse and Herman Feshbach,
*Methods of Theoretical Physics* - John David Jackson,
*Classical Electrodynamics* - Ulrich Gerlach, Linear Mathematics in Infinite Dimensions: Signals, Boundary Value Problems, and Special Functions

- Philip Morse and Herman Feshbach,
- Potential theory
- Oliver Kellogg,
*Foundations of Potential Theory* - Solomon Mikhlin,
*Integral Equations and Their Applications to Certain Problems in Mechanics, Mathematical Physics, and Technology*

- Oliver Kellogg,
- Scattering theory
- Max Born and Emil Wolf,
*Principles of Optics* - Eugen Merzbacher,
*Quantum Mechanics* - Leonard Schiff,
*Quantum Mechanics*

- Max Born and Emil Wolf,
- Scientific computation
- Germund Dahlquist and Åke Björck,
*Numerical Methods* - William Press, Saul Teukolsky, William Vetterling, and Brian Flannery, Numerical Recipes
- Eugene Tyrtyshnikov,
*A Brief Introduction to Numerical Analysis* - Yousef Saad,
*Iterative Methods for Sparse Linear Systems* - Gene Golub and Charles Van Loan,
*Matrix Computations*

- Germund Dahlquist and Åke Björck,
- Special functions
- Milton Abramowitz and Irene Stegun, eds.,
*Handbook of Mathematical Functions* - Wolfram Research, MathWorld
- Wolfram Research, Wolfram Functions Site

- Milton Abramowitz and Irene Stegun, eds.,
- Original sources
- History of Fast Multipole Methods
- Naoshi Nishimura,
"Fast multipole accelerated boundary integral equation methods,"
*Applied Mechanics Reviews*, 55 (4): 299-324, 2002.

- Naoshi Nishimura,
"Fast multipole accelerated boundary integral equation methods,"
- Volume and boundary integral equations
- Martin Kilian, "On the Riemann-Hilbert problem."

- Numerical representations of function spaces and linear operators
based on algebra
- Per-Gunnar Martinsson, Vladimir Rokhlin, and Mark Tygert, "On interpolation and integration in finite-dimensional spaces of bounded functions," CAMCoS.
- Hongwei Cheng, Zydrunas Gimbutas, Per-Gunnar Martinsson,
and Vladimir Rokhlin, "On the compression of low rank matrices,"
*SIAM Journal on Scientific Computing*, 26 (4): 1389-1404, 2005. - Ming Gu and Stanley Eisenstat, "Efficient algorithms for computing
a strong rank-revealing QR factorization,"
*SIAM Journal on Scientific Computing*, 17 (4): 848-869, 1996.

- Fast methods for applying non-oscillatory linear integral operators
- Per-Gunnar Martinsson and Vladimir Rokhlin,
"An accelerated kernel-independent Fast Multipole Method
in one dimension,"
*SIAM Journal on Scientific Computing*, 29 (3): 1160-1178, 2007. - Zydrunas Gimbutas and Vladimir Rokhlin,
"A generalized Fast Multipole Method for nonoscillatory kernels,"
*SIAM Journal on Scientific Computing*, 24 (3): 796-817, 2002. - Hongwei Cheng, Leslie Greengard, and Vladimir Rokhlin,
"A fast multipole algorithm in three dimensions,"
*Journal of Computational Physics*, 155 (2): 468-498, November 1999. - Leslie Greengard and Vladimir Rokhlin,
"A fast algorithm for particle simulations,"
*Journal of Computational Physics*, 73 (2): 325-348, December 1987.

- Per-Gunnar Martinsson and Vladimir Rokhlin,
"An accelerated kernel-independent Fast Multipole Method
in one dimension,"
- Fast methods for applying the Green operators
of time-harmonic wave equations
- Hongwei Cheng, William Crutchfield, Zydrunas Gimbutas, Leslie Greengard,
J. Frank Ethridge, Jingfang Huang, Vladimir Rokhlin, Norman Yarvin,
and Junsheng Zhao, "A wideband Fast Multipole Method for the Helmholtz
equation in three dimensions,"
*Journal of Computational Physics*, 216 (1): 300-325, July 2006.

- Hongwei Cheng, William Crutchfield, Zydrunas Gimbutas, Leslie Greengard,
J. Frank Ethridge, Jingfang Huang, Vladimir Rokhlin, Norman Yarvin,
and Junsheng Zhao, "A wideband Fast Multipole Method for the Helmholtz
equation in three dimensions,"
- Fast Plane Wave Time-Domain (PWTD) algorithm for the solution
of time-dependent wave equations
- A. Arif Ergin, Balasubramaniam Shanker, and Eric Michielssen,
"Plane-wave time-domain algorithms," chapter 18 in
Weng Cho Chew, Jian-Ming Jin, Eric Michielssen, and Jiming Song, eds.,
*Fast and Efficient Algorithms in Computational Electromagnetics*, Artech House, Boston, 2001. - A. Arif Ergin, Balasubramaniam Shanker, and Eric Michielssen,
"Plane-wave time-domain algorithm enhanced time-domain integral equation
solvers," chapter 19 in
Weng Cho Chew, Jian-Ming Jin, Eric Michielssen, and Jiming Song, eds.,
*Fast and Efficient Algorithms in Computational Electromagnetics*, Artech House, Boston, 2001. - A. Arif Ergin, Balasubramaniam Shankar, and Eric Michielssen,
"The Plane-Wave Time-Domain algorithm for the fast analysis
of transient wave phenomena,"
*IEEE Antennas and Propagation Magazine*, 41 (4): 39-52, August 1999.

- A. Arif Ergin, Balasubramaniam Shanker, and Eric Michielssen,
"Plane-wave time-domain algorithms," chapter 18 in
Weng Cho Chew, Jian-Ming Jin, Eric Michielssen, and Jiming Song, eds.,
- Direct/locally-adaptive solution techniques
- Per-Gunnar Martinsson and Vladimir Rokhlin,
"A fast direct solver for boundary integral equations in two dimensions,"
*Journal of Computational Physics*, 205 (1): 1-23, May 2005.

- Per-Gunnar Martinsson and Vladimir Rokhlin,
"A fast direct solver for boundary integral equations in two dimensions,"

- History of Fast Multipole Methods