1 |
L. Li, Double series expansions for π, AIMS Math. 6 (2021), no. 5, 5000-5007. https://doi.org/10.3934/math.2021294
DOI
|
2 |
W. Li, Lightcone expansions of conformal blocks in closed form, J. High Energy Phys. 2020, no. 6, 105, 22 pp. https://doi.org/10.1007/jhep06(2020)
|
3 |
W. Nahm, A. Recknagel, and M. Terhoeven, Dilogarithm identities in conformal field theory, Modern Phys. Lett. A 8 (1993), no. 19, 1835-1847. https://doi.org/10.1142/S0217732393001562
DOI
|
4 |
G. Nemes and A. Nemes, A note on the Landau constants, Appl. Math. Comput. 217 (2011), no. 21, 8543-8546. https://doi.org/10.1016/j.amc.2011.03.058
DOI
|
5 |
L. J. Slater, Generalized hypergeometric functions, Cambridge University Press, Cambridge, 1966.
|
6 |
M. Terhoeven, Dilogarithm identities, fusion rules and structure constants of CFTs, Modern Phys. Lett. A 9 (1994), no. 2, 133-141. https://doi.org/10.1142/S0217732394000149
DOI
|
7 |
J. G. F. Wan, Series for 1/π using Legendre's relation, Integral Transforms Spec. Funct. 25 (2014), no. 1, 1-14. https://doi.org/10.1080/10652469.2013.809072
DOI
|
8 |
J. Wan and W. Zudilin, Generating functions of Legendre polynomials: a tribute to Fred Brafman, J. Approx. Theory 164 (2012), no. 4, 488-503. https://doi.org/10.1016/j.jat.2011.12.001
DOI
|
9 |
D. Zagier, The dilogarithm function, in Frontiers in number theory, physics, and geometry. II, 3-65, Springer, Berlin, 2007. https://doi.org/10.1007/978-3-540-30308-4_1
DOI
|
10 |
G. N. Watson, The constants of Landau and Lebesgue, Quart. J. Math. Oxford Ser. 1 2 (1930), no. 3, 310-318.
DOI
|
11 |
J. T. Holdeman, Jr., Legendre polynomial expansions of hypergeometric functions with applications, J. Math. Phys. 11 (1970), 114-117. https://doi.org/10.1063/1.1665035
DOI
|
12 |
S. Ramanujan, Modular equations and approximations to π, Q. J. Math. 45 (1914), 350-372.
|
13 |
W. N. Bailey, Generalized hypergeometric series, Cambridge Tracts in Mathematics and Mathematical Physics, No. 32, Stechert-Hafner, Inc., New York, 1964.
|
14 |
J. M. Campbell, Ramanujan-like series for involving harmonic numbers, Ramanujan J. 46 (2018), no. 2, 373-387. https://doi.org/10.1007/s11139-018-9995-9
DOI
|
15 |
J. M. Campbell, J. D'Aurizio, and J. Sondow, On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions, J. Math. Anal. Appl. 479 (2019), no. 1, 90-121. https://doi.org/10.1016/j.jmaa.2019.06.017
DOI
|
16 |
H. H. Chan, J. Wan, and W. Zudilin, Legendre polynomials and Ramanujan-type series for 1/π, Israel J. Math. 194 (2013), no. 1, 183-207. https://doi.org/10.1007/s11856-012-0081-5
DOI
|
17 |
P. Levrie, Using Fourier-Legendre expansions to derive series for and , Ramanujan J. 22 (2010), no. 2, 221-230. https://doi.org/10.1007/s11139-010-9222-9
DOI
|
18 |
F. M. S. Lima, New definite integrals and a two-term dilogarithm identity, Indag. Math. (N.S.) 23 (2012), no. 1-2, 1-9. https://doi.org/10.1016/j.indag.2011.08.008
DOI
|
19 |
J. G. F. Wan, Random walks, elliptic integrals and related constants, PhD Thesis, University of Newcastle, 2013.
|
20 |
X. Wang and W. Chu, Further Ramanujan-like series containing harmonic numbers and squared binomial coefficients, Ramanujan J. 52 (2020), no. 3, 641-668. https://doi.org/10.1007/s11139-019-00140-5
DOI
|
21 |
H. Chen, Interesting series associated with central binomial coefficients, Catalan numbers and harmonic numbers, J. Integer Seq. 19 (2016), no. 1, Article 16.1.5, 11 pp.
|
22 |
B. C. Berndt, Ramanujan's Notebooks. Part IV, Springer-Verlag, New York, 1994. https://doi.org/10.1007/978-1-4612-0879-2
DOI
|
23 |
J. M. Campbell, New series involving harmonic numbers and squared central binomial coefficients, Rocky Mountain J. Math. 49 (2019), no. 8, 2513-2544. https://doi.org/10.1216/RMJ-2019-49-8-2513
DOI
|
24 |
J. M. Campbell, New families of double hypergeometric series for constants involving 1/π2, Ann. Polon. Math. 126 (2021), no. 1, 1-20. https://doi.org/10.4064/ap200709-4-1
DOI
|
25 |
J. M. Campbell and A. Sofo, An integral transform related to series involving alternating harmonic numbers, Integral Transforms Spec. Funct. 28 (2017), no. 7, 547-559. https://doi.org/10.1080/10652469.2017.1318874
DOI
|
26 |
E. R. Canfield, From recursions to asymptotics: Durfee and dilogarithmic deductions, Adv. in Appl. Math. 34 (2005), no. 4, 768-797. https://doi.org/10.1016/j.aam.2004.08.008
DOI
|
27 |
J. Horn, Ueber die Convergenz der hypergeometrischen Reihen zweier und dreier Veranderlichen, Math. Ann. 34 (1889), no. 4, 544-600. https://doi.org/10.1007/BF01443681
DOI
|
28 |
E. Landau, Abschtzung der Koeffiziententensumme einer Potenzreihe, Arch. Math. Phys. 21 (1913), 42-50.
|
29 |
W. Chu, π-formulas implied by Dougall's summation theorem for 5F4-series, Ramanujan J. 26 (2011), no. 2, 251-255. https://doi.org/10.1007/s11139-010-9274-x
DOI
|
30 |
V. S. Adamchik, A certain series associated with Catalan's constant, Z. Anal. Anwendungen 21 (2002), no. 3, 817-826. https://doi.org/10.4171/ZAA/1110
DOI
|