Digamma function (English Wikipedia)

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

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ams.org

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

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

arxiv.org

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.
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

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

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.

core.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. 137: 203–209. doi:10.4171/RSMUP/137-10.

doi.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. 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. (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.
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

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.
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

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

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

lccn.loc.gov

Gradshteyn, I. S.; Ryzhik, I. M. (2015). "8.365.5". Table of integrals, series and products. 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

"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

dlmf.nist.gov

semanticscholar.org

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

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.