In mathematics, a Ramanujan–Sato series generalizes Ramanujan's pi formulas such as, 1 π = 2 2 99 2 ∑ k = 0 ∞ ( 4 k ) ! k ! 4 26390 k + 1103 396 4 k {\displaystyle...

Theory and Computational Complexity. These two are examples of a Ramanujan–Sato series. The related Chudnovsky algorithm uses a discriminant with class...

theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable. Ramanujan initially developed...

{-163}}}{2}}\right)=-640\,320^{3}.} For similar formulas, see the Ramanujan–Sato series. For the four largest Heegner numbers, the approximations one obtains...

Wayback machine of Michael Somos' website. Chowla–Selberg formula Ramanujan–Sato series q-series Weierstrass elliptic function Partition function Kronecker limit...

This identity is similar to some of Ramanujan's formulas involving π, and is an example of a Ramanujan–Sato series. The time complexity of the algorithm...

that 22/7 exceeds π Proof of Wallis product Rabbi Nehemiah Radian Ramanujan–Sato series Rhind Mathematical Papyrus Salamin–Brent algorithm Software for...

)^{4}396^{4k}}}={\frac {9801}{2{\sqrt {2}}\pi }}} (see Srinivasa Ramanujan, Ramanujan–Sato series) The following are efficient for calculating arbitrary binary...

by Emma Haruka Iwao in 2022. For similar formulae, see also the Ramanujan–Sato series. In 2006, mathematician Simon Plouffe used the PSLQ integer relation...

\approx {\frac {9801}{2206{\sqrt {2}}}}\approx 3.14159273} See Ramanujan–Sato series. From the mid-20th century onwards, all improvements in calculation...

the Dedekind eta function η ( τ ) {\displaystyle \eta (\tau )} . Ramanujan–Sato series, level 4 Duke, William (2005), Continued Fractions and Modular Functions...

{-163}}}{2}}\right)=-640320^{3}.} For similar formulas, see the Ramanujan–Sato series. The j {\displaystyle j} -invariant is only sensitive to isomorphism...

In mathematics, the Ramanujan conjecture, due to Srinivasa Ramanujan (1916, p. 176), states that Ramanujan's tau function given by the Fourier coefficients...

theorem Ramanujan's sum Rogers–Ramanujan identities Rogers–Ramanujan continued fraction Ramanujan–Sato series Ramanujan magic square Hardy–Ramanujan Journal...

The Ramanujan tau function, studied by Ramanujan (1916), is the function τ : N → Z {\displaystyle \tau :\mathbb {N} \to \mathbb {Z} } defined by the following...

series Modular curve Ramanujan–Petersson conjecture Birch and Swinnerton-Dyer conjecture Automorphic form Selberg trace formula Artin conjecture Sato–Tate...

infinitely often. Ramanujan–Petersson conjecture: a number of related conjectures that are generalizations of the original conjecture. Sato–Tate conjecture:...

Dordrecht: Kluwer Academic Publishers. ISBN 9780792317654; OCLC 25709270 Sato, Kenichi. (2005), Kinsei Nihon Suugakushi -Seki Takakazu no jitsuzou wo motomete...

Sequencing Project". Sol Genomics Network. Retrieved 21 October 2009. Ramanujan, K. (30 January 2007). "Tomato genome project gets $1.8M". News.cornell...

early instance of such birthday magic square was created by Srinivasa Ramanujan. He created a 4×4 square in which he entered his date of birth in DD-MM-CC-YY...

Composition Factors of Monodromy Groups, Annals of Mathematics Second Series, Vol. 154, No. 2 (Sep., 2001), pp. 327–345. Published by: Mathematics Department...

the same as the area of the triangle. This concludes the proof. Following Satō Moshun (Smith & Mikami 1914, pp. 130–132), Nicholas of Cusa and Leonardo...

doi:10.1039/b813709a. PMID 19224019. Varma VB, Ray A, Wang ZM, Wang ZP, Ramanujan RV (November 2016). "Droplet Merging on a Lab-on-a-Chip Platform by Uniform...

related topics. If a = 0 or b = 0 then the Kloosterman sum reduces to the Ramanujan sum. K(a, b; m) depends only on the residue class of a and b modulo m...

Elwin, ethographer and collector of Indian folk tales (1902–1964) A. K. Ramanujan, poet and scholar of Indian literature (1929–1993) Santal Folk Tales,...

/ Yoichi Nishijima); and video game player and genius prodigy Krishna Ramanujan (Wonder-Black) (Kris Zimmerman / Orine Fukushima). The supporting characters...

Quillen Frank Quinn Paul Rabinowitz Tibor Radó M. S. Raghunathan Srinivasa Ramanujan Norman Ramsey Helena Rasiowa Douglas Ravenel Michael C. Reed David Rees...

19–23, 1999. Max-Planck-Institut für extraterrestrische Physik. Katsuhiko Sato (31 January 1999). Cosmological Parameters and the Evolution of the Universe...