Special Functions and Their Application.
This short text gives clear descriptions and explanations of the Gamma function, the Probability Integral and its related functions, Spherical Harmonics Theory, The Bessel function, Hermite polynomials and Laguerre polynomials.
Saved in:
: | |
---|---|
Place / Publishing House: | Aalborg : : River Publishers,, 2021. Ã2021. |
Year of Publication: | 2021 |
Edition: | 1st ed. |
Language: | English |
Online Access: | |
Physical Description: | 1 online resource (124 pages) |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
id |
50029002973 |
---|---|
ctrlnum |
(MiAaPQ)50029002973 (Au-PeEL)EBL29002973 (OCoLC)1289259031 |
collection |
bib_alma |
record_format |
marc |
spelling |
Koranga, Bipin Singh. Special Functions and Their Application. 1st ed. Aalborg : River Publishers, 2021. Ã2021. 1 online resource (124 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Front Cover -- Special Functions and their Applications -- Contents -- Preface -- List of Tables -- 1 The Gamma Function -- 1.1 Definition of Gamma Function -- 1.2 Gamma Function and Some Relations -- 1.3 The Logarithmic Derivative of the Gamma Function -- 1.4 Asymptotic Representation of the Gamma Function for Large |z| -- 1.5 Definite Integrals Related to the Gamma Function -- 1.6 Exercises -- 2 The Probability Integral and Related Functions -- 2.1 The Probability Integral and its Basic Properties -- 2.2 Asymptotic Representation of Probability Integral for Large |z| -- 2.3 The Probability Integral of Imaginary Argument -- 2.4 The Probability Fresnel Integrals -- 2.5 Application to Probability Theory -- 2.6 Application to the Theory of Heat Conduction -- 2.7 Application to the Theory of Vibrations -- 2.8 Exercises -- 3 Spherical Harmonics Theory -- 3.1 Introduction -- 3.2 The Hypergeometric Equation and its Series Solution -- 3.3 Legendre Functions -- 3.4 Integral Representations of the Legendre Functions -- 3.5 Some Relations Satisfied by the Legendre Functions -- 3.6 Workskian of Pairs of Solutions of Legendre's Equation -- 3.7 Recurrence Relations for the Legendre Functions -- 3.8 Associated Legendre Functions -- 3.9 Exercises -- 4 Bessel Function -- 4.1 Bessel Functions -- 4.2 Generating Function -- 4.3 Recurrence Relations -- 4.4 Orthonormality -- 4.5 Application to the Optical Fiber -- 4.6 Exercises -- 5 Hermite Polynomials -- 5.1 Hermite Functions -- 5.2 Generating Function -- 5.3 Recurrence Relations -- 5.4 Rodrigues Formula -- 5.5 Orthogonality and Normalilty -- 5.6 Application to the Simple Harmonic Oscillator -- 5.7 Exercises -- 6 Laguerre Polynomials -- 6.1 Laguerre Functions -- 6.2 Generating Function -- 6.3 Recurrence Relations -- 6.4 Rodrigues Formula -- 6.5 Orthonormality -- 6.6 Application to the Hydrogen Atom. 6.7 Associated Laguerre Polynomials -- 6.7.1 Properties of Associated Laguerre Polynomials -- 6.8 Exercises -- Bibliography -- Index -- About the Authors -- Back Cover. This short text gives clear descriptions and explanations of the Gamma function, the Probability Integral and its related functions, Spherical Harmonics Theory, The Bessel function, Hermite polynomials and Laguerre polynomials. Description based on publisher supplied metadata and other sources. Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. Functions, Special. Electronic books. Print version: Koranga, Bipin Singh Special Functions and Their Application Aalborg : River Publishers,c2021 9788770226264 ProQuest (Firm) https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=29002973 Click to View |
language |
English |
format |
eBook |
author |
Koranga, Bipin Singh. |
spellingShingle |
Koranga, Bipin Singh. Special Functions and Their Application. Front Cover -- Special Functions and their Applications -- Contents -- Preface -- List of Tables -- 1 The Gamma Function -- 1.1 Definition of Gamma Function -- 1.2 Gamma Function and Some Relations -- 1.3 The Logarithmic Derivative of the Gamma Function -- 1.4 Asymptotic Representation of the Gamma Function for Large |z| -- 1.5 Definite Integrals Related to the Gamma Function -- 1.6 Exercises -- 2 The Probability Integral and Related Functions -- 2.1 The Probability Integral and its Basic Properties -- 2.2 Asymptotic Representation of Probability Integral for Large |z| -- 2.3 The Probability Integral of Imaginary Argument -- 2.4 The Probability Fresnel Integrals -- 2.5 Application to Probability Theory -- 2.6 Application to the Theory of Heat Conduction -- 2.7 Application to the Theory of Vibrations -- 2.8 Exercises -- 3 Spherical Harmonics Theory -- 3.1 Introduction -- 3.2 The Hypergeometric Equation and its Series Solution -- 3.3 Legendre Functions -- 3.4 Integral Representations of the Legendre Functions -- 3.5 Some Relations Satisfied by the Legendre Functions -- 3.6 Workskian of Pairs of Solutions of Legendre's Equation -- 3.7 Recurrence Relations for the Legendre Functions -- 3.8 Associated Legendre Functions -- 3.9 Exercises -- 4 Bessel Function -- 4.1 Bessel Functions -- 4.2 Generating Function -- 4.3 Recurrence Relations -- 4.4 Orthonormality -- 4.5 Application to the Optical Fiber -- 4.6 Exercises -- 5 Hermite Polynomials -- 5.1 Hermite Functions -- 5.2 Generating Function -- 5.3 Recurrence Relations -- 5.4 Rodrigues Formula -- 5.5 Orthogonality and Normalilty -- 5.6 Application to the Simple Harmonic Oscillator -- 5.7 Exercises -- 6 Laguerre Polynomials -- 6.1 Laguerre Functions -- 6.2 Generating Function -- 6.3 Recurrence Relations -- 6.4 Rodrigues Formula -- 6.5 Orthonormality -- 6.6 Application to the Hydrogen Atom. 6.7 Associated Laguerre Polynomials -- 6.7.1 Properties of Associated Laguerre Polynomials -- 6.8 Exercises -- Bibliography -- Index -- About the Authors -- Back Cover. |
author_facet |
Koranga, Bipin Singh. |
author_variant |
b s k bs bsk |
author_sort |
Koranga, Bipin Singh. |
title |
Special Functions and Their Application. |
title_full |
Special Functions and Their Application. |
title_fullStr |
Special Functions and Their Application. |
title_full_unstemmed |
Special Functions and Their Application. |
title_auth |
Special Functions and Their Application. |
title_new |
Special Functions and Their Application. |
title_sort |
special functions and their application. |
publisher |
River Publishers, |
publishDate |
2021 |
physical |
1 online resource (124 pages) |
edition |
1st ed. |
contents |
Front Cover -- Special Functions and their Applications -- Contents -- Preface -- List of Tables -- 1 The Gamma Function -- 1.1 Definition of Gamma Function -- 1.2 Gamma Function and Some Relations -- 1.3 The Logarithmic Derivative of the Gamma Function -- 1.4 Asymptotic Representation of the Gamma Function for Large |z| -- 1.5 Definite Integrals Related to the Gamma Function -- 1.6 Exercises -- 2 The Probability Integral and Related Functions -- 2.1 The Probability Integral and its Basic Properties -- 2.2 Asymptotic Representation of Probability Integral for Large |z| -- 2.3 The Probability Integral of Imaginary Argument -- 2.4 The Probability Fresnel Integrals -- 2.5 Application to Probability Theory -- 2.6 Application to the Theory of Heat Conduction -- 2.7 Application to the Theory of Vibrations -- 2.8 Exercises -- 3 Spherical Harmonics Theory -- 3.1 Introduction -- 3.2 The Hypergeometric Equation and its Series Solution -- 3.3 Legendre Functions -- 3.4 Integral Representations of the Legendre Functions -- 3.5 Some Relations Satisfied by the Legendre Functions -- 3.6 Workskian of Pairs of Solutions of Legendre's Equation -- 3.7 Recurrence Relations for the Legendre Functions -- 3.8 Associated Legendre Functions -- 3.9 Exercises -- 4 Bessel Function -- 4.1 Bessel Functions -- 4.2 Generating Function -- 4.3 Recurrence Relations -- 4.4 Orthonormality -- 4.5 Application to the Optical Fiber -- 4.6 Exercises -- 5 Hermite Polynomials -- 5.1 Hermite Functions -- 5.2 Generating Function -- 5.3 Recurrence Relations -- 5.4 Rodrigues Formula -- 5.5 Orthogonality and Normalilty -- 5.6 Application to the Simple Harmonic Oscillator -- 5.7 Exercises -- 6 Laguerre Polynomials -- 6.1 Laguerre Functions -- 6.2 Generating Function -- 6.3 Recurrence Relations -- 6.4 Rodrigues Formula -- 6.5 Orthonormality -- 6.6 Application to the Hydrogen Atom. 6.7 Associated Laguerre Polynomials -- 6.7.1 Properties of Associated Laguerre Polynomials -- 6.8 Exercises -- Bibliography -- Index -- About the Authors -- Back Cover. |
isbn |
9788770226257 9788770226264 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA351 |
callnumber-sort |
QA 3351 |
genre |
Electronic books. |
genre_facet |
Electronic books. |
url |
https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=29002973 |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515.5 |
dewey-sort |
3515.5 |
dewey-raw |
515.5 |
dewey-search |
515.5 |
oclc_num |
1289259031 |
work_keys_str_mv |
AT korangabipinsingh specialfunctionsandtheirapplication |
status_str |
n |
ids_txt_mv |
(MiAaPQ)50029002973 (Au-PeEL)EBL29002973 (OCoLC)1289259031 |
carrierType_str_mv |
cr |
is_hierarchy_title |
Special Functions and Their Application. |
marc_error |
Info : Unimarc and ISO-8859-1 translations identical, choosing ISO-8859-1. --- [ 856 : z ] |
_version_ |
1792331068315009024 |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03790nam a22004213i 4500</leader><controlfield tag="001">50029002973</controlfield><controlfield tag="003">MiAaPQ</controlfield><controlfield tag="005">20240229073849.0</controlfield><controlfield tag="006">m o d | </controlfield><controlfield tag="007">cr cnu||||||||</controlfield><controlfield tag="008">240229s2021 xx o ||||0 eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9788770226257</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9788770226264</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(MiAaPQ)50029002973</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(Au-PeEL)EBL29002973</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1289259031</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">MiAaPQ</subfield><subfield code="b">eng</subfield><subfield code="e">rda</subfield><subfield code="e">pn</subfield><subfield code="c">MiAaPQ</subfield><subfield code="d">MiAaPQ</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA351</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.5</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Koranga, Bipin Singh.</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Special Functions and Their Application.</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1st ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Aalborg :</subfield><subfield code="b">River Publishers,</subfield><subfield code="c">2021.</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">Ã2021.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (124 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Front Cover -- Special Functions and their Applications -- Contents -- Preface -- List of Tables -- 1 The Gamma Function -- 1.1 Definition of Gamma Function -- 1.2 Gamma Function and Some Relations -- 1.3 The Logarithmic Derivative of the Gamma Function -- 1.4 Asymptotic Representation of the Gamma Function for Large |z| -- 1.5 Definite Integrals Related to the Gamma Function -- 1.6 Exercises -- 2 The Probability Integral and Related Functions -- 2.1 The Probability Integral and its Basic Properties -- 2.2 Asymptotic Representation of Probability Integral for Large |z| -- 2.3 The Probability Integral of Imaginary Argument -- 2.4 The Probability Fresnel Integrals -- 2.5 Application to Probability Theory -- 2.6 Application to the Theory of Heat Conduction -- 2.7 Application to the Theory of Vibrations -- 2.8 Exercises -- 3 Spherical Harmonics Theory -- 3.1 Introduction -- 3.2 The Hypergeometric Equation and its Series Solution -- 3.3 Legendre Functions -- 3.4 Integral Representations of the Legendre Functions -- 3.5 Some Relations Satisfied by the Legendre Functions -- 3.6 Workskian of Pairs of Solutions of Legendre's Equation -- 3.7 Recurrence Relations for the Legendre Functions -- 3.8 Associated Legendre Functions -- 3.9 Exercises -- 4 Bessel Function -- 4.1 Bessel Functions -- 4.2 Generating Function -- 4.3 Recurrence Relations -- 4.4 Orthonormality -- 4.5 Application to the Optical Fiber -- 4.6 Exercises -- 5 Hermite Polynomials -- 5.1 Hermite Functions -- 5.2 Generating Function -- 5.3 Recurrence Relations -- 5.4 Rodrigues Formula -- 5.5 Orthogonality and Normalilty -- 5.6 Application to the Simple Harmonic Oscillator -- 5.7 Exercises -- 6 Laguerre Polynomials -- 6.1 Laguerre Functions -- 6.2 Generating Function -- 6.3 Recurrence Relations -- 6.4 Rodrigues Formula -- 6.5 Orthonormality -- 6.6 Application to the Hydrogen Atom.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">6.7 Associated Laguerre Polynomials -- 6.7.1 Properties of Associated Laguerre Polynomials -- 6.8 Exercises -- Bibliography -- Index -- About the Authors -- Back Cover.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This short text gives clear descriptions and explanations of the Gamma function, the Probability Integral and its related functions, Spherical Harmonics Theory, The Bessel function, Hermite polynomials and Laguerre polynomials.</subfield></datafield><datafield tag="588" ind1=" " ind2=" "><subfield code="a">Description based on publisher supplied metadata and other sources.</subfield></datafield><datafield tag="590" ind1=" " ind2=" "><subfield code="a">Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. </subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Functions, Special.</subfield></datafield><datafield tag="655" ind1=" " ind2="4"><subfield code="a">Electronic books.</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Koranga, Bipin Singh</subfield><subfield code="t">Special Functions and Their Application</subfield><subfield code="d">Aalborg : River Publishers,c2021</subfield><subfield code="z">9788770226264</subfield></datafield><datafield tag="797" ind1="2" ind2=" "><subfield code="a">ProQuest (Firm)</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=29002973</subfield><subfield code="z">Click to View</subfield></datafield></record></collection> |