BBP-type formulas — An elementary approach

Simon Kristensen; Oskar Mathiasen

doi:10.1016/j.jnt.2022.09.001

BBP-type formulas — An elementary approach

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

1 Citation (Scopus)

5 Downloads (Pure)

Abstract

We provide a simple way of searching for formulas of the Bailey–Borwein–Plouffe type together with an algorithm and an implementation in sage. Aside from rediscovering some already known formulas, the method has been used in the discovery of a new BBP-type formula for 3π. In addition, the implementation is very flexible and allows us to look for BBP-type formulas to irrational bases. As an example of this, searching in various Pisot bases, we have discovered a formula for π in base 1+3, along with additional formulas.

Original language	English
Journal	Journal of Number Theory
Volume	244
Pages (from-to)	251-263
Number of pages	13
ISSN	0022-314X
DOIs	https://doi.org/10.1016/j.jnt.2022.09.001
Publication status	Published - Mar 2023

Keywords

BBP-type formulas
Formulas for π
Null formulas

Access to Document

10.1016/j.jnt.2022.09.001Licence: CC BY

1-s2.0-S0022314X22002013-mainFinal published version, 303 KBLicence: CC BY

Cite this

@article{f39a73e1b46347dbbfa2972cb4a87b6c,

title = "BBP-type formulas — An elementary approach",

abstract = "We provide a simple way of searching for formulas of the Bailey–Borwein–Plouffe type together with an algorithm and an implementation in sage. Aside from rediscovering some already known formulas, the method has been used in the discovery of a new BBP-type formula for 3π. In addition, the implementation is very flexible and allows us to look for BBP-type formulas to irrational bases. As an example of this, searching in various Pisot bases, we have discovered a formula for π in base 1+3, along with additional formulas.",

keywords = "BBP-type formulas, Formulas for π, Null formulas",

author = "Simon Kristensen and Oskar Mathiasen",

year = "2023",

month = mar,

doi = "10.1016/j.jnt.2022.09.001",

language = "English",

volume = "244",

pages = "251--263",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - BBP-type formulas — An elementary approach

AU - Kristensen, Simon

AU - Mathiasen, Oskar

PY - 2023/3

Y1 - 2023/3

N2 - We provide a simple way of searching for formulas of the Bailey–Borwein–Plouffe type together with an algorithm and an implementation in sage. Aside from rediscovering some already known formulas, the method has been used in the discovery of a new BBP-type formula for 3π. In addition, the implementation is very flexible and allows us to look for BBP-type formulas to irrational bases. As an example of this, searching in various Pisot bases, we have discovered a formula for π in base 1+3, along with additional formulas.

AB - We provide a simple way of searching for formulas of the Bailey–Borwein–Plouffe type together with an algorithm and an implementation in sage. Aside from rediscovering some already known formulas, the method has been used in the discovery of a new BBP-type formula for 3π. In addition, the implementation is very flexible and allows us to look for BBP-type formulas to irrational bases. As an example of this, searching in various Pisot bases, we have discovered a formula for π in base 1+3, along with additional formulas.

KW - BBP-type formulas

KW - Formulas for π

KW - Null formulas

UR - http://www.scopus.com/inward/record.url?scp=85140583795&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2022.09.001

DO - 10.1016/j.jnt.2022.09.001

M3 - Journal article

AN - SCOPUS:85140583795

SN - 0022-314X

VL - 244

SP - 251

EP - 263

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

BBP-type formulas — An elementary approach

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this