Consequences of Srinivasa Ramanujan integrals involving Meijer’s G-function

Showkat Ahmad Dar; Mohammad Kamarujjama; Richard Bruce Paris; Mohammad Idris Qureshi

doi:10.1515/anly-2022-1059

Consequences of Srinivasa Ramanujan integrals involving Meijer’s G-function

Showkat Ahmad Dar^*, Mohammad Kamarujjama, Richard Bruce Paris, Mohammad Idris Qureshi

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we investigate and evaluate the analytical expressions for some definite integrals of Srinivasa Ramanujan in terms of Meijer’s G-function by using the Laplace transforms of sin ⁡ (βx²), cos ⁡ (β⁢x²), x ⁢sin (βx²) and x cos (βx²). In addition, we investigate a number of infinite summation formulas involving Meijer’s G-function and closed-form evaluation of some related infinite series.

Original language	English
Pages (from-to)	49-57
Number of pages	9
Journal	Analysis (Germany)
Volume	43
Issue number	1
Early online date	10 Jan 2023
DOIs	https://doi.org/10.1515/anly-2022-1059
Publication status	Published - 1 Feb 2023

Keywords

Ramanujan’s integrals
Laplace transform
Mellin-Barnes-type contour integrals

Access to Document

10.1515/anly-2022-1059

Cite this

@article{739f021a419f48dc800c47ff0eb270cb,

title = "Consequences of Srinivasa Ramanujan integrals involving Meijer{\textquoteright}s G-function",

abstract = "In this paper, we investigate and evaluate the analytical expressions for some definite integrals of Srinivasa Ramanujan in terms of Meijer{\textquoteright}s G-function by using the Laplace transforms of sin ⁡ (βx2), cos ⁡ (β⁢x2), x ⁢sin (βx2) and x cos (βx2). In addition, we investigate a number of infinite summation formulas involving Meijer{\textquoteright}s G-function and closed-form evaluation of some related infinite series.",

author = "Dar, \{Showkat Ahmad\} and Mohammad Kamarujjama and Paris, \{Richard Bruce\} and Qureshi, \{Mohammad Idris\}",

note = "{\textcopyright} 2023 Walter de Gruyter GmbH, Berlin/Boston 2023 Meijer's G-function. Data availability statement: Not visible on the article website, VoR not available.",

year = "2023",

month = feb,

day = "1",

doi = "10.1515/anly-2022-1059",

language = "English",

volume = "43",

pages = "49--57",

journal = "Analysis (Germany)",

issn = "0174-4747",

publisher = "Walter de Gruyter GmbH",

number = "1",

}

TY - JOUR

T1 - Consequences of Srinivasa Ramanujan integrals involving Meijer’s G-function

AU - Dar, Showkat Ahmad

AU - Kamarujjama, Mohammad

AU - Paris, Richard Bruce

AU - Qureshi, Mohammad Idris

PY - 2023/2/1

Y1 - 2023/2/1

N2 - In this paper, we investigate and evaluate the analytical expressions for some definite integrals of Srinivasa Ramanujan in terms of Meijer’s G-function by using the Laplace transforms of sin ⁡ (βx2), cos ⁡ (β⁢x2), x ⁢sin (βx2) and x cos (βx2). In addition, we investigate a number of infinite summation formulas involving Meijer’s G-function and closed-form evaluation of some related infinite series.

AB - In this paper, we investigate and evaluate the analytical expressions for some definite integrals of Srinivasa Ramanujan in terms of Meijer’s G-function by using the Laplace transforms of sin ⁡ (βx2), cos ⁡ (β⁢x2), x ⁢sin (βx2) and x cos (βx2). In addition, we investigate a number of infinite summation formulas involving Meijer’s G-function and closed-form evaluation of some related infinite series.

U2 - 10.1515/anly-2022-1059

DO - 10.1515/anly-2022-1059

M3 - Article

SN - 0174-4747

VL - 43

SP - 49

EP - 57

JO - Analysis (Germany)

JF - Analysis (Germany)

IS - 1

ER -

Consequences of Srinivasa Ramanujan integrals involving Meijer’s G-function

Abstract

Keywords

Access to Document

Fingerprint

Cite this