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$P_{n}(x)$ is the Taylor polynomial of degree n centered at x = a

Taylor Polynomial of Degree n Approximation: f(x) for x near a ^[1]
$f(x)\approx P_{n}(x)=$
$f(a) f'(a)(x-a) {\frac {f''(a)}{2!}}(x-a)^{2} \cdots {\frac {f^{(n)}(a)}{n!}}(x-a)^{n}$

The Binomial Series
For: $-1<x<1$
$(1 x)^{p}=\left\{1 px {\frac {p(p-1)}{2!}}\cdot x^{2} {\frac {p(p-1)(p-2)}{3!}}\cdot x^{3} \cdots \right\}$

References, Citations, Sources, etc.

§ Openly Accessible

Astronomy OpenStax Textbook ^[2] ^[3]

Introduction to Molecular Spectroscopy from the Internet Archive ^[4]

Letter from Rome, Scanned PDF(archived) ^[5]

Fantastic content that makes you want the information for yourself, or maybe you just want to see where it is from. ^[a]

§ Accessible Citations

^ Letter, page 56

§ Accessible Citation Sources

Letter from Rome. Volume 3905 of Harvard Risorgimento preservation microfilm project (PDF). Rome, Italy: Catholic Publication House. 1871. Archived from the original on 22 Feb 2017 – via Archive.org. {{cite book}}: External link in |via= (help)

§ Textbooks

Multi Variable Calculus Text ^[1]

Hughes-Hallett, Deborah; McCallum, William G.; Gleason, Andrew M. (2013), Calculus : Single and Multivariable (6 ed.), John Wiley & Sons, ISBN 978-0470-88861-2

§ Random PDF

JSTOR Evidence in United States vs. Aaron Swartz ^[6]

§ Other Books

Einstein's Brainchild: Relativity Made Relatively Easy!^[7]

Invisible Universe: Story of Radio Astronomy ^[8]

Spectroscopy: The Key to the Stars: Reading the Lines in Stellar Spectra ^[9]

RefList

^ ^a ^b Hughes-Hallett, Deborah; McCallum, William G.; Gleason, Andrew M. (2013). Calculus : Single and Multivariable (6 ed.). John wiley. ISBN 978-0470-88861-2.
^ Fraknoi, Andrew, Morrison, David OpenStax, Astronomy. OpenStax. 13 October 2016. <http://cnx.org/content/col11992/latest/>
^ Fraknoi, Andrew; Morrison, David (13 October 2016). "OpenStax Astronomy".{{cite web}}: CS1 maint: year (link)
^ Barrow, Gordon M. (1962). Introduction to Molecular Spectroscopy (Scanned PDF). McGraw-Hill. LCCN 62-12478.
^ Letter from Rome. Volume 3905 of Harvard Risorgimento preservation microfilm project (PDF). Rome, Italy: Catholic Publication House. 1871. Archived from the original on 22 Feb 2017 – via Archive.org. {{cite book}}: External link in |via= (help)
^ JSTOR (30 July 2013). "JSTOR Evidence in United States vs. Aaron Swartz" (PDF). Archived from the original (PDF-1.6) on 1 March 2017 – via Archive.org. {{cite web}}: External link in |via= (help)
^ Parker, Barry R. (2000). Einstein's Brainchild: Relativity Made Relatively Easy!. Prometheus Books. ISBN 9781615923687.
^ Vershuur, Gerrit L. (2007). The Invisible Universe: The Story of Radio Astronomy (2 ed.). Springer Science Business Media, LLC. ISBN 978-0387-30816-6. LCCN 2006924881.
^ Robinson, Keith (2007). Spectroscopy: The Key to the Stars: Reading the Lines in Stellar Spectra. Patrick Moore's Practical Astronomy Series. Springer Science & Business Media. ISBN 9780387682884.

[6] Letter, page 56

[Hughes-1] Hughes-Hallett, Deborah; McCallum, William G.; Gleason, Andrew M. (2013). Calculus : Single and Multivariable (6 ed.). John wiley. ISBN 978-0470-88861-2.

[openastro-2] Fraknoi, Andrew, Morrison, David OpenStax, Astronomy. OpenStax. 13 October 2016. <http://cnx.org/content/col11992/latest/>

[open-astro-3] Fraknoi, Andrew; Morrison, David (13 October 2016). "OpenStax Astronomy".{{cite web}}: CS1 maint: year (link)

[4] Barrow, Gordon M. (1962). Introduction to Molecular Spectroscopy (Scanned PDF). McGraw-Hill. LCCN 62-12478.

[letterRome-5] Letter from Rome. Volume 3905 of Harvard Risorgimento preservation microfilm project (PDF). Rome, Italy: Catholic Publication House. 1871. Archived from the original on 22 Feb 2017 – via Archive.org. {{cite book}}: External link in |via= (help)

[jstor-evidence-7] JSTOR (30 July 2013). "JSTOR Evidence in United States vs. Aaron Swartz" (PDF). Archived from the original (PDF-1.6) on 1 March 2017 – via Archive.org. {{cite web}}: External link in |via= (help)

[8] Parker, Barry R. (2000). Einstein's Brainchild: Relativity Made Relatively Easy!. Prometheus Books. ISBN 9781615923687.

[Vershuur-9] Vershuur, Gerrit L. (2007). The Invisible Universe: The Story of Radio Astronomy (2 ed.). Springer Science Business Media, LLC. ISBN 978-0387-30816-6. LCCN 2006924881.

[Robinson-keith-10] Robinson, Keith (2007). Spectroscopy: The Key to the Stars: Reading the Lines in Stellar Spectra. Patrick Moore's Practical Astronomy Series. Springer Science & Business Media. ISBN 9780387682884.

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