Digamma function (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Digamma function" in English language version.

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16doi.org

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6semanticscholar.org

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6arxiv.org

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4jstor.org

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3nist.gov

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3harvard.edu

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2loc.gov

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1sfu.ca

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1wolfram.com

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1core.ac.uk

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1archive.org

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1colgate.edu

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1maa.org

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1uv.es

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1ams.org

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1worldcat.org

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1buffalo.edu

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ams.org (Global: 451^st place; English: 277^th place)

Alzer, Horst (1997). "On Some Inequalities for the Gamma and Psi Functions" (PDF). Mathematics of Computation. 66 (217): 373–389. doi:10.1090/S0025-5718-97-00807-7. JSTOR 2153660.

archive.org (Global: 6^th place; English: 6^th place)

Pairman, Eleanor (1919). Tables of the Digamma and Trigamma Functions. Cambridge University Press. p. 5.

arxiv.org (Global: 69^th place; English: 59^th place)

Blagouchine, Ia. V. (2018). "Three Notes on Ser's and Hasse's Representations for the Zeta-functions" (PDF). INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A: 1–45. arXiv:1606.02044. Bibcode:2016arXiv160602044B. doi:10.5281/zenodo.10581385.
Blagouchine, Ia. V. (2016). "Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to $π -1$ ". Journal of Mathematical Analysis and Applications. 442: 404–434. arXiv:1408.3902. Bibcode:2014arXiv1408.3902B. doi:10.1016/J.JMAA.2016.04.032. S2CID 119661147.
Blagouchine, Iaroslav V. (2014). "A theorem for the closed-form evaluation of the first generalized Stieltjes constant at rational arguments and some related summations". Journal of Number Theory. 148: 537–592. arXiv:1401.3724. doi:10.1016/j.jnt.2014.08.009.
Guo, Bai-Ni; Qi, Feng (2014). "Sharp inequalities for the psi function and harmonic numbers". Analysis. 34 (2). arXiv:0902.2524. doi:10.1515/anly-2014-0001. S2CID 16909853.
Mathar, R. J. (2004). "Chebyshev series expansion of inverse polynomials". Journal of Computational and Applied Mathematics. 196 (2): 596–607. arXiv:math/0403344. doi:10.1016/j.cam.2005.10.013. App. E
Mező, István (2014). "A note on the zeros and local extrema of Digamma related functions". arXiv:1409.2971 [math.CV].

buffalo.edu (Global: 4,241^st place; English: 2,850^th place)

cse.buffalo.edu

Beal, Matthew J. (2003). Variational Algorithms for Approximate Bayesian Inference (PDF) (PhD thesis). The Gatsby Computational Neuroscience Unit, University College London. pp. 265–266.

colgate.edu (Global: low place; English: 9,382^nd place)

math.colgate.edu

Blagouchine, Ia. V. (2018). "Three Notes on Ser's and Hasse's Representations for the Zeta-functions" (PDF). INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A: 1–45. arXiv:1606.02044. Bibcode:2016arXiv160602044B. doi:10.5281/zenodo.10581385.

core.ac.uk (Global: 1,734^th place; English: 1,312^th place)

Alzer, Horst; Jameson, Graham (2017). "A harmonic mean inequality for the digamma function and related results" (PDF). Rendiconti del Seminario Matematico della Università di Padova. 137: 203–209. doi:10.4171/RSMUP/137-10.

doi.org (Global: 2^nd place; English: 2^nd place)

Alzer, Horst; Jameson, Graham (2017). "A harmonic mean inequality for the digamma function and related results" (PDF). Rendiconti del Seminario Matematico della Università di Padova. 137: 203–209. doi:10.4171/RSMUP/137-10.
Mező, István; Hoffman, Michael E. (2017). "Zeros of the digamma function and its Barnes G-function analogue". Integral Transforms and Special Functions. 28 (11): 846–858. doi:10.1080/10652469.2017.1376193. S2CID 126115156.
Blagouchine, Ia. V. (2018). "Three Notes on Ser's and Hasse's Representations for the Zeta-functions" (PDF). INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A: 1–45. arXiv:1606.02044. Bibcode:2016arXiv160602044B. doi:10.5281/zenodo.10581385.
Blagouchine, Ia. V. (2016). "Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to $π -1$ ". Journal of Mathematical Analysis and Applications. 442: 404–434. arXiv:1408.3902. Bibcode:2014arXiv1408.3902B. doi:10.1016/J.JMAA.2016.04.032. S2CID 119661147.
Blagouchine, Iaroslav V. (2014). "A theorem for the closed-form evaluation of the first generalized Stieltjes constant at rational arguments and some related summations". Journal of Number Theory. 148: 537–592. arXiv:1401.3724. doi:10.1016/j.jnt.2014.08.009.
Choi, Junesang; Cvijovic, Djurdje (2007). "Values of the polygamma functions at rational arguments". Journal of Physics A. 40 (50): 15019. Bibcode:2007JPhA...4015019C. doi:10.1088/1751-8113/40/50/007. S2CID 118527596.
Jensen, J. L. W. V.; Gronwall, T. H. (1916). "An elementary exposition of the theory of the Gamma Function". Ann. Math. 17 (3): 124–166. doi:10.2307/2007272. JSTOR 2007272.
Bernardo, José M. (1976). "Algorithm AS 103 psi(digamma function) computation" (PDF). Applied Statistics. 25: 315–317. doi:10.2307/2347257. JSTOR 2347257.
Alzer, Horst (1997). "On Some Inequalities for the Gamma and Psi Functions" (PDF). Mathematics of Computation. 66 (217): 373–389. doi:10.1090/S0025-5718-97-00807-7. JSTOR 2153660.
Elezović, Neven; Giordano, Carla; Pečarić, Josip (2000). "The best bounds in Gautschi's inequality". Mathematical Inequalities & Applications (2): 239–252. doi:10.7153/MIA-03-26.
Guo, Bai-Ni; Qi, Feng (2014). "Sharp inequalities for the psi function and harmonic numbers". Analysis. 34 (2). arXiv:0902.2524. doi:10.1515/anly-2014-0001. S2CID 16909853.
Laforgia, Andrea; Natalini, Pierpaolo (2013). "Exponential, gamma and polygamma functions: Simple proofs of classical and new inequalities". Journal of Mathematical Analysis and Applications. 407 (2): 495–504. doi:10.1016/j.jmaa.2013.05.045.
Alzer, Horst; Jameson, Graham (2017). "A harmonic mean inequality for the digamma function and related results" (PDF). Rendiconti del Seminario Matematico della Università di Padova. 70 (201): 203–209. doi:10.4171/RSMUP/137-10. ISSN 0041-8994. LCCN 50046633. OCLC 01761704. S2CID 41966777.
Wimp, Jet (1961). "Polynomial approximations to integral transforms". Math. Comp. 15 (74): 174–178. doi:10.1090/S0025-5718-61-99221-3. JSTOR 2004225.
Mathar, R. J. (2004). "Chebyshev series expansion of inverse polynomials". Journal of Computational and Applied Mathematics. 196 (2): 596–607. arXiv:math/0403344. doi:10.1016/j.cam.2005.10.013. App. E
Hermite, Charles (1881). "Sur l'intégrale Eulérienne de seconde espéce". Journal für die reine und angewandte Mathematik (90): 332–338. doi:10.1515/crll.1881.90.332. S2CID 118866486.

harvard.edu (Global: 18^th place; English: 17^th place)

ui.adsabs.harvard.edu

Blagouchine, Ia. V. (2018). "Three Notes on Ser's and Hasse's Representations for the Zeta-functions" (PDF). INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A: 1–45. arXiv:1606.02044. Bibcode:2016arXiv160602044B. doi:10.5281/zenodo.10581385.
Blagouchine, Ia. V. (2016). "Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to $π -1$ ". Journal of Mathematical Analysis and Applications. 442: 404–434. arXiv:1408.3902. Bibcode:2014arXiv1408.3902B. doi:10.1016/J.JMAA.2016.04.032. S2CID 119661147.
Choi, Junesang; Cvijovic, Djurdje (2007). "Values of the polygamma functions at rational arguments". Journal of Physics A. 40 (50): 15019. Bibcode:2007JPhA...4015019C. doi:10.1088/1751-8113/40/50/007. S2CID 118527596.

jstor.org (Global: 26^th place; English: 20^th place)

Jensen, J. L. W. V.; Gronwall, T. H. (1916). "An elementary exposition of the theory of the Gamma Function". Ann. Math. 17 (3): 124–166. doi:10.2307/2007272. JSTOR 2007272.
Bernardo, José M. (1976). "Algorithm AS 103 psi(digamma function) computation" (PDF). Applied Statistics. 25: 315–317. doi:10.2307/2347257. JSTOR 2347257.
Alzer, Horst (1997). "On Some Inequalities for the Gamma and Psi Functions" (PDF). Mathematics of Computation. 66 (217): 373–389. doi:10.1090/S0025-5718-97-00807-7. JSTOR 2153660.
Wimp, Jet (1961). "Polynomial approximations to integral transforms". Math. Comp. 15 (74): 174–178. doi:10.1090/S0025-5718-61-99221-3. JSTOR 2004225.

lancs.ac.uk (Global: low place; English: 8,698^th place)

eprints.lancs.ac.uk

Alzer, Horst; Jameson, Graham (2017). "A harmonic mean inequality for the digamma function and related results" (PDF). Rendiconti del Seminario Matematico della Università di Padova. 70 (201): 203–209. doi:10.4171/RSMUP/137-10. ISSN 0041-8994. LCCN 50046633. OCLC 01761704. S2CID 41966777.

loc.gov (Global: 70^th place; English: 63^rd place)

lccn.loc.gov

Gradshteyn, I. S.; Ryzhik, I. M. (2015). "8.365.5". Table of integrals, series and products. Elsevier Science. ISBN 978-0-12-384933-5. LCCN 2014010276.
Alzer, Horst; Jameson, Graham (2017). "A harmonic mean inequality for the digamma function and related results" (PDF). Rendiconti del Seminario Matematico della Università di Padova. 70 (201): 203–209. doi:10.4171/RSMUP/137-10. ISSN 0041-8994. LCCN 50046633. OCLC 01761704. S2CID 41966777.

maa.org (Global: 3,479^th place; English: 2,444^th place)

"Leonhard Euler's Integral: An Historical Profile of the Gamma Function" (PDF). Archived (PDF) from the original on 2014-09-12. Retrieved 11 April 2022.

nist.gov (Global: 355^th place; English: 454^th place)

dlmf.nist.gov

semanticscholar.org (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

Mező, István; Hoffman, Michael E. (2017). "Zeros of the digamma function and its Barnes G-function analogue". Integral Transforms and Special Functions. 28 (11): 846–858. doi:10.1080/10652469.2017.1376193. S2CID 126115156.
Blagouchine, Ia. V. (2016). "Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to $π -1$ ". Journal of Mathematical Analysis and Applications. 442: 404–434. arXiv:1408.3902. Bibcode:2014arXiv1408.3902B. doi:10.1016/J.JMAA.2016.04.032. S2CID 119661147.
Choi, Junesang; Cvijovic, Djurdje (2007). "Values of the polygamma functions at rational arguments". Journal of Physics A. 40 (50): 15019. Bibcode:2007JPhA...4015019C. doi:10.1088/1751-8113/40/50/007. S2CID 118527596.
Guo, Bai-Ni; Qi, Feng (2014). "Sharp inequalities for the psi function and harmonic numbers". Analysis. 34 (2). arXiv:0902.2524. doi:10.1515/anly-2014-0001. S2CID 16909853.
Alzer, Horst; Jameson, Graham (2017). "A harmonic mean inequality for the digamma function and related results" (PDF). Rendiconti del Seminario Matematico della Università di Padova. 70 (201): 203–209. doi:10.4171/RSMUP/137-10. ISSN 0041-8994. LCCN 50046633. OCLC 01761704. S2CID 41966777.
Hermite, Charles (1881). "Sur l'intégrale Eulérienne de seconde espéce". Journal für die reine und angewandte Mathematik (90): 332–338. doi:10.1515/crll.1881.90.332. S2CID 118866486.

sfu.ca (Global: 3,413^th place; English: 2,445^th place)

math.sfu.ca

Abramowitz, M.; Stegun, I. A., eds. (1972). "6.3 psi (Digamma) Function.". Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (10th ed.). New York: Dover. pp. 258–259.

uv.es (Global: 4,591^st place; English: 9,880^th place)

Bernardo, José M. (1976). "Algorithm AS 103 psi(digamma function) computation" (PDF). Applied Statistics. 25: 315–317. doi:10.2307/2347257. JSTOR 2347257.

web.archive.org (Global: 1^st place; English: 1^st place)

"Leonhard Euler's Integral: An Historical Profile of the Gamma Function" (PDF). Archived (PDF) from the original on 2014-09-12. Retrieved 11 April 2022.

wolfram.com (Global: 513^th place; English: 537^th place)

mathworld.wolfram.com

Weisstein, Eric W. "Digamma function". MathWorld.

worldcat.org (Global: 5^th place; English: 5^th place)

search.worldcat.org

Alzer, Horst; Jameson, Graham (2017). "A harmonic mean inequality for the digamma function and related results" (PDF). Rendiconti del Seminario Matematico della Università di Padova. 70 (201): 203–209. doi:10.4171/RSMUP/137-10. ISSN 0041-8994. LCCN 50046633. OCLC 01761704. S2CID 41966777.

Digamma function (English Wikipedia)

ams.org (Global: 451st place; English: 277th place)

archive.org (Global: 6th place; English: 6th place)

arxiv.org (Global: 69th place; English: 59th place)

buffalo.edu (Global: 4,241st place; English: 2,850th place)

cse.buffalo.edu

colgate.edu (Global: low place; English: 9,382nd place)

math.colgate.edu

core.ac.uk (Global: 1,734th place; English: 1,312th place)

doi.org (Global: 2nd place; English: 2nd place)

harvard.edu (Global: 18th place; English: 17th place)