Special
Functions : Selected Topics
Proceeding of the First Annual Conference of the
Society for Special Functions and their Applications
Jodhpur (India), March 34, 2000
Editors: P. K. Banerji
Scientific Publishers, Jodhpur, India. 2000
CONTENTS
Forewords
Preface
Chandrashekar Adiga, R.Y. Denis, K.R. Vasuki
On some Continued Fraction Expansions for Ratios of 2
M.I. Qureshi, M.S. Khan, M.A. Pathan
Applications of saalschiitz’s Theorem in Hypergeometric Transformation
Involving Quarter and Unit Arguments.
D.N. Vyas
Dirchlet Average and a New Class of Hypergeometric Function
M.A. Pathan, Subuhi Khan
Generating Relations Involving Hypergeometric Functions by Means of
Integral Operators II
A.K. Agarwal, B. Dutta
Number Theory and Special Functions
S.B. Joshi
Certain Subclasses of Univalent Functions with Negative Coefficients
Deshna Loonker
On a Distributional Transform
R.K. Kumbhat, Yogesh Sharma
On Certain Distortion Theorem for Fractional Integral Operators
Manisha Dalbhide, B.I. Dave
A General Inversion Pair – II
D. Pandey
Evaluation of Multiple Integral Identities Involving Tricomi Functions
Using Groups Representation Theory
Abha Purohit
Excavating Index Transform
R.Y. Denis, S.N. Singh
Certain Results Involving qSeries and Continued Fractions
P.L. Sethi, Poonam
Generalized 2/2 Distribution of Matrix Argument and its Application in
Reliability Theory
M.A. Hussain
Some Generating Relation of Orthogonal Functions
R.Y. Denis, S.N. Singh, N.A Bhagirathi
On Certain Bilateral qSeries and Ramanujans Continued Fraction
P.L. Sethi, Shalini Varhney
On Functional Relation of Matrix Argument
Gamal N. Shenan
Application of Differintegral Operator of Arbitrary Order to a Nested
Class of Analytic Functions with Negative Coefficients
R.K. Kumbhat, Arif M. Khan
A convolution Transformation for HFunction and its Inversion
A.S.A. Galiz
On a Theory of Operator for the Modulus Function Space
R.K. Yadav, Sunita Vyas
On a Basic Analogue of the GFunction
P.L. Sethi, Vandana Rajwani
Some Bivariate Integral Equations and their Connection with Dual
Integral equations
R.K. Kumbhat, Hafiz Khan
Solution of Integral equation of Fredholm Type
R.K. Kumbhat, Seema Singhal
An Inversion Formula of Fractional Integral Operator Involving
Kummer’s Confluent Hypergeometric Function of Matrix Argument
Padmavathamma, Ruby Salestina, M.
A Note on Some Partition Identities  II
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Proceeding of
the International Conference on
Special Functions and their Applications
(Second Annual Conference) Vol. I
Lucknow (India), February 24, 2001.
Editors: R. Y. Denis, M. A. Pathan
CONTENTS
Preface
Foreword
S. Bhargava
Presidential Address (General)
S. Bhargava
Presidential Address (Technical)
R.P. Agarwal
An attempt towards presenting an unified theory for mock theta functions
S. Kanemitsu, Y. Tanigawa and M. Yoshimoto
On ZetaandLfunction values at special rational arguments via the
modular relation
J. Van der Jeugt
The invariance groups of certain single and double hypergeometric series
M.V. Subbarao
Partitions – Some parity problems and results
R.S. Pathak and S.M. Tripathi
Bailey’s integral and associated convolution operators
M.A. Pathan
On generalization of Graftype addition Theorems
Remy Y. Denis and S.N. Singh
Cayley and Orr type identities
K. Srinivasa Rao
The 3nj Coefficients and multiple hypergeometric series
Arun Verma
Identities in Ramanujan’s ‘Lost’ note book and quadratic
transformation of qseries
C.M. Joshi and Sadhna Nalwaya
On bounds of incomplete LipschitzHankel integrals of cylindrical
functions
P.K. Banerji
Differential operators of arbitrary order and nested class of analytic
functions
M.A. Hussain
Orthogonal polynomials ad their applications.
H.S.P. Srivastava
On multi index Hermite polynomials
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Proceeding of the International
Conference on
Special Functions and their Applications
(Second Annual Conference) Vol. II
Lucknow (India), February 24, 2001.
Editors: R. Y. Denis, M. A. Pathan
H.C. Khare
Special functions and their applications
Pankaj Srivastava
A page from Ramanujan’s ‘Lost’ note book
M. Kamarujjama and M. Khursheed Alam
Some generating relations involving MittagLeffeler’s Functions of
matrix variate
P.L. Sethi and
Laplace transform of biorthogonal distribution functions of matrix
theory
P.L. Sethi and Poonam
Inversion formulas for infinite generalized Toeplitz Matrices – II
P.K. Banerji and Deshna Loonker
On the Mellin transform of tempered Boehmian
P.K. Banerji and Abha Purohit
On the mapping properties of an index integral Transform of L_{p}
– spaces
Rashmi Jain and M.A. Pathan
On theorems involving Laplace transform and Weyl Fractional integral
operator
M.A. Pathan and Subuhi Khan
Representation of a Lie algebra K_{5} and Hermite Polynomials
S.S. Tak and G.S. Sisodia
Viscous heating in unsteady free convection along a Hot vertical plate
suddenly set in motion in presence of transverse magnetic field
S.S. Tak and Govind Pathak
Unsteady free convection along a hot vertical accelerated plate in
presence of transverse magnetic field
M.I. Qureshi, N.U. Khan and M.A. Pathan
Multiple Gaussian hypergeometric transformation Formula associated with
Preece result
R.K. Kumbhat and Arif M.Khan
Mellin convolution and Ifunction transformations
R.K. Kumbhat and Arif M. Khan
A regularized approximate solution of the fractional Integral operator
Pankaj Mathur
(0,2)* interpolation on nonuniformly distributed zeros on unit circle
R.K. Kumbhat and Hafiz Khan
Certain class of Mac Robert’s fractional integrals
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Selected
Topics in Special Functions
Editors: R. P. Agarwal, H. L. Manocha, K.
Srinivasa Rao
Allied Publishers Limited, New Delhi. 2001
CONTENTS
Preface
Acknowledgements
R.P. Agarwal
Recent Developments in the Theory of Generalized Hypergeometric series
H.L. Manocha
Lie Theory, qDifference Calculus and qFunctions
S. Bhargava
Cubic Theta Functions
A. Verma
Polybasic Hypergeometric Series
K. Srinivasa Rao
Hypergeometric series and Quantum Theory of Angular Momentum
A,K. Agarwal
Some Applications of Special Functions in Number Theory and
Combinatorics
M.A. Pathan
Lie Theory and Generalized Bessel Functions
R.Y. Denis and S.N. Singh
Generalized Hypergeometric Functions And Continued Fractions
C.Adiga and D.D. Somashekara
Rogers – Ramanujan Identities, Continued Fractions and their
Generalizations
R.S. Pathak
Special Functions and Distributions
Vivek Sahai
Euler integral transformation, its qanalogue and Special functions
using Lie theory and quantum theory
P.K. Banerji
Fractional Differintegrals
R.K. Saxena
On the Unification and Extension of Univariate And Bivariate
Distributions Associated with special Functions
C.M. Joshi
Exact asymptotic coefficients and bounds of generalized hypergeometric
function
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Proceeding of the Third Annual
Conference of the
Society for Special Functions and their Applications
Varansi (India), March 46, 2002
Editors: R. S. Pathak, A. K. Agarwal, M. A. Pathan
CONTENTS
Preface
Foreword
B.D. Agrawal
Professor Brij Mohan : A Biography
N.K. Thakare
Some Open Problems in the Theory of Biorthogonal Polynomials
A.K. Agarwal
New Combinatorial Interpretations of Some Analytical Identities
K. Srinivasa Rao
Numerical Aspects of Special Functions
R. Rangarajan, E.R. Suryanarayan and Rangaswamy
Properties of Brahmagupta Polynomials with Two Parameters
N. Shiva Kumar
On a Paper of Srinivasa Ramanujan
R.K. Saxena
Certain Properties of Generalized MittagLeffler Function
M.I. Qureshi, M. Sadiq Khan and M.A. Pathan
Some Families of Gaussian Hypergeometric Generating Relations
Mohannad J.S. Shahwan
Lie Theoretic Generating Functions of TwoIndex Modified Generalized
Bessel Functions
Dhaneshwar Pandey
Realization of Representations of Subgroups and Evaluation of Some
Integral Identities.
P.K. Banerji
Fractional Calculus and Analytic Functions
R.K. Saxena, Jeta Ram and (Ms) A.R. Chauhan
Fractional Integration of Appell Function F3 Associated with General
Class of Multivariable Polynomials.
M.K. Ahamad
Diamond Wavelets and TimeFrequency Representation
H.S.P. Srivastava
Multivariable Bessel Polynomials
Mridula Garg, Girish Mishra, Mahesh Kumar Gupta
Distribution of the Ratio of Products of Rational Powers of Independent
Random Variables.
Satya Prakash Singh
Certain Transformation Formulae for Basic Hypergeometric Series
R.Y. Denis and S.N. Singh
Transformations of PolyBasic Hypergeometric Functions
R.S. Pathak and S.M. Tripathi
The Generalized Hankel Convolutions on Distribution Spaces
J. Das (n,ee Chaudhuri)
The Solutions of Some Real Linear Self adjoint nth Order Ordinary
Differential Equations
Jayasri Sett and A.K. Biswas
On Some Properties of Hill’s Equations with Three Terms
Pitambar Das
On Oscillatory Behavior of Neutral Delay Differential Equations
S.P. Singh and D. Mishra
Certain Partition Theorems of Rogers Ramanujan Type
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Proceeding of
the Fourth Annual Conference of the
Society for Special Functions and their Applications
Jaipur (India), March 46, 2003
Editors: A. K. Agarwal, M. A. Pathan, S. P. Goel
CONTENTS
Preface
K. Takano
On The Infinite Divisibility of Normed Conjugate Product of Gamma
Function
A. K. Agarwal
An Analogue of a Rogers Ramanujan Identity
A. Bernarini, G. Dattoli and P. E. Ricci
L  Exponential and Higher Order Laguerre Polynomials
S. P. Goel and J. K. Prajapat
New Class of Analytic Functions Involving Certain Fractional
DifferIntegral Operator
S. P. Singh
On Certain Transformations Involving qSeries
Pankaj Srivastava and Bindu Prakash Mishra
Ramanujan Sum of _{1}y_{1 }and
its Applications
Mridula Gerg and Vimal Katta
On Study of a Partial Differential Equation Governing the Transport of
Heavy Pollutant From the Ground Level Aerial Sources
using the Generalized Hankel Transform
Trilok Mathur
Convolution of an Integral Equation Involving Multiple Integration with
a Product of Confuelent Hypergeometric Function
Asit Kumar Sarkar
A Unified Group Theoretic Method on Improper Partial QusaiBilateral
Generating Function Involving Some Special Cases
Mridula Gerg and Amit Mathur
Finite Integral Involving Leguerre Functions and the H  Function
Rashmi Jain and Arti Sharma
A Study of H  Function Transform
Shashikant, Sonia Sharma and A. K. Rathie
Some Summation Formulas for Appell's Functions F_{1}
S. S. Bhati and Meenakshi Purohit
The Confluent Hypergeometric Function of Four Variables
Alka Parashar
On a General Multiple Eulerian Involving General Classes of Polynomials
and Multivariable H  Functions
Subuhi Khan and Ghazala Yasmin
On Generating Relation Involving Laguerre 2D Functions
S. Ahamd Ali
An Infinite Family of Mock Theta Functions
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Proceeding of
the Fifth Annual Conference of the
Society for Special Functions and their Applications
Lucknow (India), February 8 10, 2004
Editors: A. K. Agarwal, R. P. Agarwal, N. K.
Thakare, M. A. Pathan, R. Y. Denis, S. Ahmad Ali
CONTENTS
Preface
Arun Verma
Presidential Address
D. Karp, A. Savenkova and Saitnik
Series Expansions and Asymptotics for Incomplete Elliptic Integrals
via Partial Fraction Decompositions
Mridula Gerg and Shweta Mittal
Study of a Generalization of multivariable Bessel Polynomials
H. S. P. Srivastava
MultiindexMultivariable Sister Celine Polynomials
Swaroop Nandan Bora
Associated Legendre Polynomials in the Problems of Water Wave
Diffraction by Submerged Bodies
R. K. Yadav abd S. D. Purohit
qLaplace Transforms of Certain Generalized Basic Hypergeometric
Functions
Partha Pratim Dey
Multiplier Theorem Revisited
M. Kamarujjama and Dinesh Singh
On Certain Integral Transforms Associated with Lauricella Functions
Padmavathamma, R. Raghavendra and B. M.
ChandraShekhara
A New Partition Function
Subhash Chandra Maratha and Swaroop Nandan Bora
Bessel Functions in Linear Water Wave Diffraction Theory
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Proceeding of
the Sixth Annual Conference of the
Society for Special Functions and their Applications
Jaunpur (India), June 4 5, 2005
Editors: R. P. Agarwal, N. K. Thakare, M. A.
Pathan, R. Y. Denis, S. N. Singh
CONTENTS
Preface
R. S. Pathak
Presidential Address
G. Dattoli, M. R. Martinelli and P. E. Ricci
Comments on Operational Methods and Diffusion Problems
R. Y. Denis, S. N. Singh and S. P. Singh
Certain Transformations of qHypergeometric Functions with Uncoonected
Bases
S. P. Goel and Manita Bhagtani
On Certan Family of Generalized Integral Operators and Multivalent
Analytic Functions
Mumtaz Ahmad Khan, M. P. Singh and Ajay Kumar Shukla
Solution of Miscible Fluid Flow Through Porous Media in Terms of
Hypergeometric Funtion 0F1
Rajiv K. Srivastava
Bicomlex Analysis : A Prospective Generalization for the Theory of
Special Functions
Rashmi Jain and Rajani Agarwal
A Study of Unified Operators and the HFunction Transform
P. N. Rathie and A. K. Rathei
Gauss Hypergeometric Function and Generalization of Matchbox Problem of
Banach
S. P. Singh
Certain Results Involving Ramanujan's tau Functions
Shaun Cooper and Syeda Noor Fathima
Symmetry of Cubic Theta Function
A. K. Agarwal
Lattice Path and Mock Theta Functions
Chena Ram and Naresh
Fourier Series Associated with a General Class of Multivariable
Polynomials and the IFunction
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Proceeding of
the Seventh Annual Conference of the
Society for Special Functions and their Applications
Pune (India), February 21 23, 2006
Editors: A. K. Agarwal, N. K. Thakare, M. A.
Pathan, B. N. Waphare, M. M. Shikare
CONTENTS
Preface
N. K. Thakre
A Reports
C. M. Joshi
Applications of CertainMethods in the Analytical Derivation of Rogers
Ramanujan Identities and their Generalizations
Pushpa N. Rathie, Chang C. Y. Doerea and RAul
Matsushita
Levy Distribution, HFunction and Application to Currency Data
Mridula Gerg and Alka Rao
An Extention of Fractional Free Electron Laser Equation
Padmavathamma, Raghvendra, R, and Rajeshkanna, M. R.
Bijection Proof of a New Partition Identity
Rashmi Jain, Kantesh Fupta and Rajani Agarwal
Finite Summation Formula Involving Lauricella Series
P. K. Baneji
An Introduction to Beohmians and their Transforms
R. Y. Denis, S. N. Singh and S. P. Singh
On Simple Proofs of Certain Entries from Ramanujan's Second Notebook
Mumtaz Ahmad Khan and Mukesh Pal Singh
On General Class of Polynomials of Three Variables
Mridula Gerg and Kumkum Jain
Some New Representation for Voiget Functions
N. U. Khan
Certain Generating Functions Involving Mutivariable Hypergeometric
Polynomials
S. P. Singh
Continued Fractions Related to some Theta and Partition Functions
J. P. Yadav
On Certain Continued Fraction Involving Basic Bilateral Series
A. K. Shukla
Generalization of Class of Polynomials Connected with MittagLeffler
Function
A. M. Mathai
A Review of Recent Developments on Generalized Complex Matrix Variat
Drichlet Integrals
Proceeding of
the
Eighth
Annual Conference of the
Society for Special Functions and their Applications
Pala (India), May 18 20, 2007
Editors: A. M. Mathai, M. A. Pathan, K. K. Jose, Joy
Jacob
CONTENTS
Preface
A.K. Agarwal
Presidential Address
Hans J. Haubold
Special Functions and Pathways for
Statistical Problems
in Astrophysics: An Essay in
Honour of A.M. Mathai
Camila C.S. Caiado and Pushpa N.
Rathie
Polynomial Coefficients and Distribution of
the Sum of
Discrete Uniform Variables
K.K. Jose, Ancy Joseph and
Miroslav M. Ristic
A Generalized Bivariate SemiPareto
Minification Process
R.K. Saxena
On a Unified Inverse Gaussian Distribution
Mumtaz Ahmad Khan and Bhagwat
Swaroop Sharma
A Study of Three Variables Analogues of
Certain
Fractional Integral Operators
A. Hasanov
A New Class of Confluent Hypergeometric
Functions with
Three Variables
Mumtaz Ahmad Khan and Bijan Rouhi
On Three Variable Analogue of Gegenbaur
Polynomials
Lishamol Tomy and K.K. Jose
On a Convolution of Normal and Generalized SemiLaplace
Distributions and its
Applications in Time Series Modelling
M.I. Qureshi, Aas Mohammad and
Kaleem A. Quraishi
Analysis of the SliderCrank Mechanism Using
Hypergeometric Approach
Satya Prakash Singh
A Note on Bailey’s Transform
K.K. Jose and Shanoja R. Naik
On qWeibull
Distribution and its Applications in Survival and
Reliability Analysis
P. Uma and K.K. Jose
Generalized MittagLeffler Distributions and
Processes
G. Girija
Some Fundamental Special Functions on A2
and their Properties
K.V. Jayamol and K.K. Jose
a.p.g.f Ordering:
Characterizations and Equivalence Properties
Alice Thomas, K.K. Jose, Miroslav
M. Risti´c and Ancy Joseph
MarshallOlkin Univariate and Bivariate
Logistic Processes
A.K. Shukla and J.C. Prajapati
On Explicit Representations and Integral
Transformations of General
Class of Polynomials
M.A. Pathan, B.B. Jaimini and
Shiksha Gautam
On a General Class of Euler Type Integrals
Hemant Kumar, M. A. Pathan and
Shilesh Kumari
On Some Kernels of Integral Functions,
Multiple Fractional Integral
Operators Involving these Kernels and Applications
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