Monotonicity properties of the generalized Struve functions

Rosihan M. Ali; Saiful R. Mondal; Kottakkaran S. Nisar

doi:10.4134/JKMS.j160137

Monotonicity properties of the generalized Struve functions

Rosihan M. Ali
, Saiful R. Mondal
, Kottakkaran S. Nisar

Mathematics

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

13 Scopus citations

Abstract

This paper introduces and studies a generalization of the classical Struve function of order p given by (Formula Presented.) Representation formulae are derived for _aS_p,c. Further the function _aS_p,cis shown to be a solution of an (a+1)-order differential equation. Monotonicity and log-convexity properties for the generalized Struve function _aS_p,care investigated, particulary for the case c = −1. As a consequence, Turán-type inequalities are established. For a = 2 and c = −1, dominant and subordinant functions are obtained for the Struve function ₂S_p,−1.

Original language	English
Pages (from-to)	575-598
Number of pages	24
Journal	Journal of the Korean Mathematical Society
Volume	54
Issue number	2
DOIs	https://doi.org/10.4134/JKMS.j160137
State	Published - 2017

Keywords

Bessel function
Dominant
Generalized struve function
Monotonicity properties
Turán-type inequality

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10.4134/JKMS.j160137

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title = "Monotonicity properties of the generalized Struve functions",

abstract = "This paper introduces and studies a generalization of the classical Struve function of order p given by (Formula Presented.) Representation formulae are derived for aSp,c. Further the function aSp,cis shown to be a solution of an (a+1)-order differential equation. Monotonicity and log-convexity properties for the generalized Struve function aSp,care investigated, particulary for the case c = −1. As a consequence, Tur{\'a}n-type inequalities are established. For a = 2 and c = −1, dominant and subordinant functions are obtained for the Struve function 2Sp,−1.",

keywords = "Bessel function, Dominant, Generalized struve function, Monotonicity properties, Tur{\'a}n-type inequality",

author = "Ali, \{Rosihan M.\} and Mondal, \{Saiful R.\} and Nisar, \{Kottakkaran S.\}",

note = "Publisher Copyright: {\textcopyright} 2017 Korean Mathematical Society.",

year = "2017",

doi = "10.4134/JKMS.j160137",

language = "English",

volume = "54",

pages = "575--598",

journal = "Journal of the Korean Mathematical Society",

issn = "0304-9914",

publisher = "Korean Mathematical Society",

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TY - JOUR

T1 - Monotonicity properties of the generalized Struve functions

AU - Ali, Rosihan M.

AU - Mondal, Saiful R.

AU - Nisar, Kottakkaran S.

PY - 2017

Y1 - 2017

N2 - This paper introduces and studies a generalization of the classical Struve function of order p given by (Formula Presented.) Representation formulae are derived for aSp,c. Further the function aSp,cis shown to be a solution of an (a+1)-order differential equation. Monotonicity and log-convexity properties for the generalized Struve function aSp,care investigated, particulary for the case c = −1. As a consequence, Turán-type inequalities are established. For a = 2 and c = −1, dominant and subordinant functions are obtained for the Struve function 2Sp,−1.

AB - This paper introduces and studies a generalization of the classical Struve function of order p given by (Formula Presented.) Representation formulae are derived for aSp,c. Further the function aSp,cis shown to be a solution of an (a+1)-order differential equation. Monotonicity and log-convexity properties for the generalized Struve function aSp,care investigated, particulary for the case c = −1. As a consequence, Turán-type inequalities are established. For a = 2 and c = −1, dominant and subordinant functions are obtained for the Struve function 2Sp,−1.

KW - Bessel function

KW - Dominant

KW - Generalized struve function

KW - Monotonicity properties

KW - Turán-type inequality

UR - https://www.scopus.com/pages/publications/85014056507

U2 - 10.4134/JKMS.j160137

DO - 10.4134/JKMS.j160137

M3 - Article

AN - SCOPUS:85014056507

SN - 0304-9914

VL - 54

SP - 575

EP - 598

JO - Journal of the Korean Mathematical Society

JF - Journal of the Korean Mathematical Society

IS - 2

ER -

Monotonicity properties of the generalized Struve functions

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Keywords

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