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...

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...

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...

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

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

notebook Ramanujan's master theorem Ramanujan's sum Rogers–Ramanujan identities Rogers–Ramanujan continued fraction Ramanujan–Sato series Ramanujan magic...

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

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

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

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

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

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

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

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

{\displaystyle k=1} Ramanujan–Petersson conjecture: a number of related conjectures that are generalizations of the original conjecture. Sato–Tate conjecture:...

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

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,...

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 D–M–C-Y...

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...

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

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...

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...