### Abstract

On two pages in his lost notebook, Ramanujan recorded several theorems involving the modified Bessel function Kν (z). These include Koshliakov's formula and Guinand's formula, both connected with the functional equation of nonanalytic Eisenstein series, and both discovered by these authors several years after Ramanujan's death. Other formulas, including one by K. Soni and two particularly elegant new results, are also stated without proof by Ramanujan. In this paper, we prove all the formulas claimed by Ramanujan on these two pages and conclude with a survey of related results.

Original language | English |
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Title of host publication | SURVEYS IN NUMBER THEORY |

Editors | KRISHNASWAMI ALLADI |

Pages | 21-42 |

Number of pages | 22 |

DOIs | |

Publication status | Published - 2008 Dec 1 |

### Publication series

Name | Developments in Mathematics |
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Volume | 17 |

ISSN (Print) | 1389-2177 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*SURVEYS IN NUMBER THEORY*(pp. 21-42). (Developments in Mathematics; Vol. 17). https://doi.org/10.1007/978-0-387-78510-3_2

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*SURVEYS IN NUMBER THEORY.*Developments in Mathematics, vol. 17, pp. 21-42. https://doi.org/10.1007/978-0-387-78510-3_2

**Koshliakov's formula and Guinand's formula in Ramanujan's lost notebook.** / Berndt, Bruce C.; Lee, Yoonbok; Sohn, Jaebum.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Koshliakov's formula and Guinand's formula in Ramanujan's lost notebook

AU - Berndt, Bruce C.

AU - Lee, Yoonbok

AU - Sohn, Jaebum

PY - 2008/12/1

Y1 - 2008/12/1

N2 - On two pages in his lost notebook, Ramanujan recorded several theorems involving the modified Bessel function Kν (z). These include Koshliakov's formula and Guinand's formula, both connected with the functional equation of nonanalytic Eisenstein series, and both discovered by these authors several years after Ramanujan's death. Other formulas, including one by K. Soni and two particularly elegant new results, are also stated without proof by Ramanujan. In this paper, we prove all the formulas claimed by Ramanujan on these two pages and conclude with a survey of related results.

AB - On two pages in his lost notebook, Ramanujan recorded several theorems involving the modified Bessel function Kν (z). These include Koshliakov's formula and Guinand's formula, both connected with the functional equation of nonanalytic Eisenstein series, and both discovered by these authors several years after Ramanujan's death. Other formulas, including one by K. Soni and two particularly elegant new results, are also stated without proof by Ramanujan. In this paper, we prove all the formulas claimed by Ramanujan on these two pages and conclude with a survey of related results.

UR - http://www.scopus.com/inward/record.url?scp=84859480694&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859480694&partnerID=8YFLogxK

U2 - 10.1007/978-0-387-78510-3_2

DO - 10.1007/978-0-387-78510-3_2

M3 - Chapter

AN - SCOPUS:84859480694

SN - 9780387785097

T3 - Developments in Mathematics

SP - 21

EP - 42

BT - SURVEYS IN NUMBER THEORY

A2 - ALLADI, KRISHNASWAMI

ER -