By Frank W. J. Olver, Roderick S. C. Wong.

Online text: dlmf.nist.gov/2.5

By Tom M. Apostol.

Online text: dlmf.nist.gov/27.9

Part of Chapter 27, Functions of Number Theory, credited to T. M. Apostol. The site version release date is not treated as the chapter publication year.

By Karl Dilcher.

Online text: dlmf.nist.gov/24

By Nico M. Temme.

Online text: dlmf.nist.gov/3.5#iv

Cited passages: NIST Digital Library of Mathematical Functions, §3.5(iv), equation 3.5.15 and the following discussion of nodes and weights.

By Nico M. Temme.

Online text: dlmf.nist.gov/3.5#i

Cited passages: NIST Digital Library of Mathematical Functions, §3.5(i), equation 3.5.1 and its C² hypothesis; the source writes integral minus rule; NIST Digital Library of Mathematical Functions, §3.5(i), equations 3.5.2–3.5.3: composite formula and signed error.

Chapter authors: Ranjan Roy, Frank W. J. Olver, Richard A. Askey, Roderick S. C. Wong, William P. Reinhardt. Their names are given on the official chapter landing page.

Online text: dlmf.nist.gov/1

Cited section: dlmf.nist.gov/1.10

Cited passages: §1.10(iv), equation 1.10.9, states the argument principle; equation 1.10.10 gives the multiplicity-weighted sum of zero locations minus pole locations used in the weighted argument principle.

Cited passage: §1.11(ii), equation 1.11.10, gives the coefficient relations used in elementary symmetric polynomial.

Additional cited passages: §1.13(i), equations 1.13.1–1.13.6, common equation, Wronskian, Abel identity and fundamental-pair equivalence; §1.13(iii), equations 1.13.8–1.13.10, normalized inhomogeneous equation and variation of parameters. Inspected online release: version 1.2.8, 15 September 2026; this is a reference release date, not the original chapter publication date. The source uses analytic coefficients on a simply connected complex domain.

Additional cited section: §1.2(ii) Finite Series, equation 1.2.10 and last-term definition. The five contributors credited above are Chapter 1 authors, not whole-reference authors. Inspected release: version 1.2.8, 15 September 2026; this is an online reference release date.

Additional cited section: §1.7(i), equation 1.7.2, and §1.7(ii), equation 1.7.5, including equality conditions. The existing five chapter contributors remain the Chapter 1 authors; no new publication or release date is inferred.

Additional cited section: §1.4(v), Functions of Bounded Variation, equations 1.4.33–1.4.34 and the conditions on the derivative integral. The existing five chapter contributors remain the Chapter 1 authors; no new chapter publication date is inferred.

Online text: webbook.nist.gov/cgi/cbook.cgi?Name=tert-Amyl+bromide&Units=SI

Cited passages: NIST Chemistry WebBook, Butane, 2-bromo-2-methyl-: formula and other names.

Online text: www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm

Cited passages: §1.3.5.11, Alternative Definition of Kurtosis, normal baseline and software convention warning.

Online text: www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm

Cited passages: Section 1.3.5.16, Characteristics and Limitations, items 1 and 3; Definition; Section 1.3.5.16, Critical Values: alternative scalings must match the statistic; Section 1.3.5.16, Definition and Technical Note: the formula must include both i/n and (i-1)/n.

By Richard Fitzpatrick.

Online text: farside.ph.utexas.edu/teaching/336k/lectures/node49.html

Online section revision dated 31 March 2011.

Online text: farside.ph.utexas.edu/teaching/336k/Newtonhtml/node66.html

Cited passages: Richard Fitzpatrick, Newtonian Dynamics, Matrix Eigenvalue Theory, repeated-eigenvalue discussion following equation 484.

Online text: farside.ph.utexas.edu/teaching/336k/Newtonhtml/node67.html

Cited passages: Richard Fitzpatrick, Newtonian Dynamics, Principal Axes of Rotation, equations 487–490.

Online text: farside.ph.utexas.edu/teaching/336k/Newtonhtml/node65.html

Cited passages: Richard Fitzpatrick, Newtonian Dynamics, Rotational Kinetic Energy, equations 467–471.