Arun Verma

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All published works

Action	Title	Year	Authors
+ PDF Chat	Understanding the Relationship between Prompts and Response Uncertainty in Large Language Models	2024	Z. Zhang Arun Verma Finale Doshi‐Velez Bryan Kian Hsiang Low
+	A Preconditioned Conjugate Gradient Approach to Linear Equality	2003	Thomas F. Coleman Arun Verma
+ PDF Chat	ADMIT-1	2000	Thomas F. Coleman Arun Verma
+ PDF Chat	Efficient Calculation of Jacobian and Adjoint Vector Products in the Wave Propagational Inverse Problem Using Automatic Differentiation	2000	Thomas F. Coleman Fadil Santosa Arun Verma
+ PDF Chat	The Efficient Computation of Sparse Jacobian Matrices Using Automatic Differentiation	1998	Thomas F. Coleman Arun Verma
+ PDF Chat	Structure and Efficient Hessian Calculation	1998	Thomas F. Coleman Arun Verma
+	Structured automatic differentiation	1998	Arun Verma Thomas F. Coleman
+	Semi-Automatic Differentiation	1998	Thomas F. Coleman Fadil Santosa Arun Verma
+	On the Efficient Methods to Solve ODEs and BVPs Using Automatic Differentiation	1996	Arun Verma
+	Structure and Efficient Jacobian Calculation	1996	Thomas F. Coleman Arun Verma
+ PDF Chat	Quadratic transformation formulas for basic hypergeometric series	1993	Mizan Rahman Arun Verma
+	On the Geronimus polynomial sets	1988	W. A. Al‐Salam Arun Verma
+ PDF Chat	Infinite sum of products of continuous $q$-ultraspherical functions	1987	Mizan Rahman Arun Verma
+	A q-integral representation of Rogers' q-ultraspherical polynomials and some applications	1986	Mizan Rahman Arun Verma
+	Product and Addition Formulas for the Continuous <i>q</i>-Ultraspherical Polynomials	1986	Mizan Rahman Arun Verma
+ PDF Chat	<i>q</i>-Konhauser polynomials	1983	W. A. Al‐Salam Arun Verma
+	Some Remarks on q-Beta Integral	1982	W. A. Al-Salam Arun Verma
+ PDF Chat	Some remarks on $q$-beta integral	1982	W. A. Al‐Salam Arun Verma
+	A Quadratic Transformation of a Basic Hypergeometric Series	1980	Arun Verma
+ PDF Chat	Certain Summation Formulae for Basic Hypergeometric Series	1977	Arun Verma
+ PDF Chat	On product of generalized Appell polynomials	1975	Arun Verma
+ PDF Chat	A fractional Leibniz $q$-formula	1975	W. A. Al‐Salam Arun Verma
+ PDF Chat	On generating functions of classical polynomials	1974	Arun Verma
+	Characterizations of $\sigma $-Type Zero Polynomial Sets	1972	Arun Verma
+	On σ-type polynomials generated by A(t)ψ(xH(t))	1972	Arun Verma
+	Fibonacci Numbers and Eulerian Polynomials	1971	W. A. Al‐Salam Arun Verma
+	Generalized Sheffer polynomials	1970	W. A. Al‐Salam Arun Verma
+ PDF Chat	Generalized basic hypergeometric series with unconnected bases (II)’	1970	Ravi P. Agarwal Arun Verma
+ PDF Chat	A Transformation Connecting Products of Generalised Basic Hypergeometric Functions	1968	Arun Verma
+	Generalized basic hypergeometric series with unconnected bases	1967	Ravi P. Agarwal Arun Verma
+ PDF Chat	A note on expansions involving Meijer’s 𝐺-functions	1967	Arun Verma
+ PDF Chat	A note on the summation of the generalised hypergeometric functions	1967	Arun Verma
+ PDF Chat	Expansions involving hypergeometric functions of two variables	1966	Arun Verma
+ PDF Chat	Certain expansions of the basic hypergeometric functions	1966	Arun Verma
+ PDF Chat	A note on an expansion of hypergeometric functions of two variables	1966	Arun Verma
+	A Class of Expansions of G-Functions and the Laplace Transform	1965	Arun Verma
+ PDF Chat	A class of expansions of 𝐺-functions and the Laplace transform	1965	Arun Verma
+ PDF Chat	Series involving products of two E-functions	1964	Arun Verma
+	Certain expansions of generalised basic hypergeometric functions	1964	Arun Verma
+	General expansions involvingE-functions	1964	Arun Verma

Common Coauthors

Coauthor	Papers Together
Thomas F. Coleman	8
W. A. Al‐Salam	6
Mizan Rahman	3
Ravi P. Agarwal	2
Fadil Santosa	2
Finale Doshi‐Velez	1
Mizan Rahman	1
Bryan Kian Hsiang Low	1
Z. Zhang	1
W. A. Al-Salam	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	The Efficient Computation of Sparse Jacobian Matrices Using Automatic Differentiation	1998	Thomas F. Coleman Arun Verma	5
+	A Class of Expansions of G-Functions and the Laplace Transform	1965	Arun Verma	5
+	Structure and Efficient Jacobian Calculation	1996	Thomas F. Coleman Arun Verma	5
+	On the Transformation Theory of Basic Hypergeometric Functions	1951	D. B. Sears	5
+ PDF Chat	Structure and Efficient Hessian Calculation	1998	Thomas F. Coleman Arun Verma	4
+	Generalized Hypergeometric Functions	1966	Y. L. L. L. J. Slater	4
+ PDF Chat	Expansions of Hypergeometric Functions in Hypergeometric Functions	1961	Jerry L. Fields Jet Wimp	4
+ PDF Chat	The Cyclic Coloring Problem and Estimation of Sparse Hessian Matrices	1986	Thomas F. Coleman Jin‐Yi Cai	4
+	Computing Large Sparse Jacobian Matrices Using Automatic Differentiation	1994	Brett M. Averick Jorge J. Morè Christian Bischof Alan Carle Andreas Griewank	4
+ PDF Chat	Expansions of hypergeometric functions in hypergeometric functions	1961	Jerry L. Fields Jet Wimp	4
+	Expansion formulas for generalized hypergeometric functions	1962	Jet Wimp Yudell L. Luke	4
+	Transformations of Basic Hypergeometric Functions of Special Type	1950	D. B. Sears	4
+	Computing Gradients in Large-Scale Optimization Using Automatic Differentiation	1997	Christian Bischof Ali Bouaricha Peyvand M. Khademi Jorge J. Morè	4
+	Computing a sparse Jacobian matrix by rows and columns	1998	A. K. M. Shahadat Hossain Trond Steihaug	3
+ PDF Chat	Software for estimating sparse Jacobian matrices	1984	Thomas F. Coleman B. S. Garbow Jorge J. Morè	3
+	On the Estimation of Sparse Jacobian Matrices	1974	A. R. Curtis M. J. D. Powell John Reid	3
+ PDF Chat	Estimation of sparse hessian matrices and graph coloring problems	1984	Thomas F. Coleman Jorge J. Morè	3
+	A generalization of ultraspherical polynomials	1983	Richard Askey Mourad E. H. Ismail	3
+	Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials	1985	Richard Askey James Wilson	3
+	Estimation of Sparse Jacobian Matrices and Graph Coloring Blems	1983	Thomas F. Coleman Jorge J. Morè	3
+	On the Estimation of Sparse Hessian Matrices	1979	M. J. D. Powell Philippe L. Toint	3
+ PDF Chat	A class of expansions of 𝐺-functions and the Laplace transform	1965	Arun Verma	3
+	Some Bounds on the Complexity of Gradients, Jacobians, and Hessians	1993	Andreas Griewank	2
+	Rogers’ Linearization Formula for the Continuous <i>q</i>-Ultraspherical Polynomials and Quadratic Transformation Formulas	1985	George Gasper	2
+	Expansion Theorems for the G-Function. III	1953	C.S. Meijer	2
+	Another q-Extension of the Beta Function	1981	George E. Andrews Richard Askey	2
+	Semi-Automatic Differentiation	1998	Thomas F. Coleman Fadil Santosa Arun Verma	2
+	<i>Generalized Hypergeometric Functions</i>	1967	L. J. Slater Werner C. Rheinboldt	2
+	Beiträge zur Theorie der Heineschen Reihen. Die 24 Integrale der hypergeometrischen <i>q</i>‐Differenzengleichung. Das <i>q</i>‐Analogon der Laplace‐Transformation	1949	Wolfgang Hahn	2
+ PDF Chat	A class of methods for solving nonlinear simultaneous equations	1965	C. G. Broyden	2
+ PDF Chat	Orthogonal Polynomials	1971		2
+	Computational differentiation : techniques, applications, and tools	1996	Martin Berz	2
+	SERIES OF HYPERGEOMETRIC TYPE WHICH ARE INFINITE IN BOTH DIRECTIONS	1936	W. N. Bailey	2
+	An Analysis of Inverse Heat Transfer Problems With Phase Changes Using an Integral Method	1988	Nicholas Zabaras Subrata Mukherjee Oliver P. Richmond	2
+	Some Transformations of Generalized Hypergeometric Series	1927	F. J. W. Whipple	2
+	Some formulas of F. H. Jackson	1969	L. Carlitz	2
+	On <i>q</i>-Analogues of the Watson and Whipple Summations	1976	George E. Andrews	2
+	EXPANSIONS OF APPELL'S DOUBLE HYPERGEOMETRIC FUNCTIONS	1940	J. L. Burchnall T. W. Chaundy	2
+	Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation	1992	Andreas Griewank	2
+	Positivity of the Poisson Kernel for the Continuous <i>q</i>-Jacobi Polynomials and Some Quadratic Transformation Formulas for Basic Hypergeometric Series	1986	George Gasper Mizan Rahman	2
+ PDF Chat	Another 𝑞-extension of the beta function	1981	George E. Andrews Richard Askey	2
+	Transformations of non-terminating basic hypergeometric series, their contour integrals and applications to Rogers-Ramanujan identities	1982	Aman Verma V. K. Jain	2
+ PDF Chat	The Linearization of the Product of Continuous <sub>q</sub>-Jacobi Polynomials	1981	Mizan Rahman	2
+	EXPANSIONS OF HYPERGEOMETRIC FUNCTIONS	1942	T. W. Chaundy	2
+	Product Formulas of Watson, Bailey and Bateman Types and Positivity of the Poisson Kernel for <i>q</i>-Racah Polynomials	1984	George Gasper Mizan Rahman	2
+	Asymptotic and generating relations for the q-Jacobi and 4φ3 polynomials	1982	Mourad E. H. Ismail James Wilson	1
+ PDF Chat	Über die hypergeometrische Reihe . (Fortsetzung).	1836	E.E. Kummer	1
+	Enumeration of Partitions: The Role of Eulerian Series and q-Orthogonal Polynomials	1977	George E. Andrews Richard Askey	1
+ PDF Chat	Expansions involving hypergeometric functions of two variables	1966	Arun Verma	1
+	ON CONTOUR INTEGRALS FOR THE PRODUCT OF TWO BESSEL FUNCTIONS	1935	S. O. Rice	1