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Academic literature on the topic 'Generalized Legendre's associated function'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Generalized Legendre's associated function"

1

Yashwant, Singh, and Kumar Mandia Harmendra. "ON AN EXPANSION FORMULA FOR THE MULTIVARIABLE I - FUNCTION INVOLVING GENERALIZED LEGENDRE'S ASSOCIATED FUNCTION." International Journal of Research – Granthaalayah 4, no. 1 (2017): 55–62. https://doi.org/10.5281/zenodo.848169.

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The authors have established a new expansion formula for multivariable I -function due to Prasad [5] in terms of products of the multivariable I -function and the generalized Legendre’s associated function due to Meulenbeld [3]. Some special cases are given in the last.

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Virchenko, N. A. "Applications of Legendre's generalized associated functions." Ukrainian Mathematical Journal 39, no. 2 (1987): 124–30. http://dx.doi.org/10.1007/bf01057490.

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Ayant, F. Y. "On an expansion formula for the multivariable aleph-function involving generalized Legendre's associated function." International Journal of Mathematics Trends and Technology 33, no. 1 (2016): 67–73. http://dx.doi.org/10.14445/22315373/ijmtt-v33p510.

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Singh, Yashwant, and Harmendra Kumar Mandia. "ON AN EXPANSION FORMULA FOR THE MULTIVARIABLE -FUNCTION INVOLVING GENERALIZED LEGENDRE’S ASSOCIATED FUNCTION." International Journal of Research -GRANTHAALAYAH 4, no. 1 (2016): 55–62. http://dx.doi.org/10.29121/granthaalayah.v4.i1.2016.2843.

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The authors have established a new expansion formula for multivariable -function due to Prasad [5] in terms of products of the multivariable -function and the generalized Legendre’s associated function due to Meulenbeld [3]. Some special cases are given in the last.

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Ayant, Frédéric. "An expansion formula for multivariable Gimel-function involving generalized Legendre Associated function." International Journal of Mathematics Trends and Technology 56, no. 4 (2018): 223–28. http://dx.doi.org/10.14445/22315373/ijmtt-v56p532.

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Cohl, Howard S., and Diego E. Dominici. "Generalized Heine’s identity for complex Fourier series of binomials." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2126 (2010): 333–45. http://dx.doi.org/10.1098/rspa.2010.0222.

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In his treatise, Heine ( Heine 1881 In Theorie und Anwendungen ) gave an identity for the Fourier series of the function , with , and z >1, in terms of associated Legendre functions of the second kind . In this paper, we generalize Heine’s identity for the function , with , and , in terms of . We also compute closed-form expressions for some .

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Dassani*, Mamta, and Mukesh kushwaha. "Some Generalized Results to unify Classical Polynomials." International Journal of Basic Sciences and Applied Computing 3, no. 3 (2021): 1–5. http://dx.doi.org/10.35940/ijbsac.b0201.033321.

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Present work of this paper deals with the unification of classical polynomials in which we have defined a generalized polynomial set analogous to that of associated Legendre polynomial P (x) m n by taking 5the use of Operator. Also we have derived explicit form, Operational Formulae generating functions for this function.

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MamtaDassani and kushwaha Mukesh. "Some Generalized Results to unify Classical Polynomials." International Journal of Basic Sciences and Applied Computing (IJBSAC) 3, no. 3 (2021): 1–5. https://doi.org/10.35940/ijbsac.B0201.033321.

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Present work of this paper deals with the unification of classical polynomials in which we have defined a generalized polynomial set analogous to that of associated Legendre polynomial P (x) m n by taking 5the use of Operator. Also we have derived explicit form, OperationalFormulae generating functions for this function.

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Ayant, Frédéric. "A Study of Unified Fractional Integral Operator Involving Generalized Laguerre Function and (т,ᵦ)-Generalized Associated Legendre Function". International Journal of Mathematics Trends and Technology 61, № 2 (2018): 117–23. http://dx.doi.org/10.14445/22315373/ijmtt-v61p517.

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Roditty-Gershon, Edva, Chris Hall та Jonathan P. Keating. "Variance of sums in arithmetic progressions of divisor functions associated with higher degree L-functions in 𝔽q[t]". International Journal of Number Theory 16, № 05 (2019): 1013–30. http://dx.doi.org/10.1142/s1793042120500529.

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We compute the variances of sums in arithmetic progressions of generalized [Formula: see text]-divisor functions related to certain [Formula: see text]-functions in [Formula: see text], in the limit as [Formula: see text]. This is achieved by making use of recently established equidistribution results for the associated Frobenius conjugacy classes. The variances are thus expressed, when [Formula: see text], in terms of matrix integrals, which may be evaluated. Our results extend those obtained previously in the special case corresponding to the usual [Formula: see text]-divisor function, when

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Books on the topic "Generalized Legendre's associated function"

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Iryna, Fedotova, ed. Generalized associated Legendre functions and their applications. World Scientific, 2001.

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Virchenko, Nina, and Iryna Fedotova. Generalized Associated Legendre Functions and Their Applications. World Scientific Publishing Co Pte Ltd, 2001.

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Virchenko, Nina, and Iryna Fedotova. Generalized Associated Legendre Functions and Their Applications. World Scientific Publishing Co Pte Ltd, 2001.

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Swartz, Johnna R., Lisa M. Shin, Brenda Lee, and Ahmad R. Hariri. Using Facial Expressions to Probe Brain Circuitry Associated With Anxiety and Depression. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190613501.003.0014.

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Emotional facial expressions are processed by a distributed corticolimbic brain circuit including the amygdala, which plays a central role in detecting and responding to emotional expressions, and the prefrontal cortex, which evaluates, integrates, and regulates responses to emotional expressions. Using functional magnetic resonance imaging (fMRI) to probe circuit function can reveal insights into the pathophysiology of mood and anxiety disorders. In this chapter, we review fMRI research into corticolimbic circuit processing of emotional facial expressions in social anxiety disorder, posttraum

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Horing, Norman J. Morgenstern. Interacting Electron–Hole–Phonon System. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0011.

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Chapter 11 employs variational differential techniques and the Schwinger Action Principle to derive coupled-field Green’s function equations for a multi-component system, modeled as an interacting electron-hole-phonon system. The coupled Fermion Green’s function equations involve five interactions (electron-electron, hole-hole, electron-hole, electron-phonon, and hole-phonon). Starting with quantum Hamilton equations of motion for the various electron/hole creation/annihilation operators and their nonequilibrium average/expectation values, variational differentiation with respect to particle s

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Winkler, Carol, and Kareem El Damanhoury. Proto-State Media Systems. Oxford University Press, 2022. http://dx.doi.org/10.1093/oso/9780197568026.001.0001.

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Proto-State Media Systems explores how militant, non-state organizations create, develop, and sustain media systems in the contemporary environment. It challenges generalized applications of dominant state-based media system models by revealing how such approaches lack full explanatory power for assessing the structures and functions of media systems of groups like al-Qaeda and ISIS. Utilizing theories of constitutive discourse and online networks, as well as revised conceptualizations of proto-states and media systems, the book explores how militant proto-states can create identity-based medi

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Book chapters on the topic "Generalized Legendre's associated function"

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Britvina, Lyubov. "Hankel Generalized Convolutions with the Associated Legendre Functions in the Kernel and Their Applications." In Trends in Mathematics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-35914-0_3.

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Raj, Kuldip, and Kavita Saini. "Intuitionistic Fuzzy Generalized Lucas Ideal Convergent Sequence Spaces Associated with Orlicz Function." In Soft Computing Techniques in Engineering, Health, Mathematical and Social Sciences. CRC Press, 2021. http://dx.doi.org/10.1201/9781003161707-10.

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Marichal, Jean-Luc, and Naïm Zenaïdi. "Applications to Some Standard Special Functions." In A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95088-0_10.

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AbstractWe now apply our results to certain multiple Γ-type functions and multiple $$\log \Gamma $$ log Γ -type functions that are known to be well-studied special functions, namely: the gamma function, the digamma function, the polygamma functions, the q-gamma function, the Barnes G-function, the Hurwitz zeta function and its higher order derivatives, the generalized Stieltjes constants, and the Catalan number function. For recent background on some of these functions, see, e.g., Srivastava and Choi (Zeta andq-zeta functions and associated series and integrals. Elsevier, Amsterdam, 2012).

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Diestmann, Thomas, Nils Broedling, Benedict Götz, and Tobias Melz. "Surrogate Model-Based Uncertainty Quantification for a Helical Gear Pair." In Lecture Notes in Mechanical Engineering. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-77256-7_16.

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AbstractCompetitive industrial transmission systems must perform most efficiently with reference to complex requirements and conflicting key performance indicators. This design challenge translates into a high-dimensional multi-objective optimization problem that requires complex algorithms and evaluation of computationally expensive simulations to predict physical system behavior and design robustness. Crucial for the design decision-making process is the characterization, ranking, and quantification of relevant sources of uncertainties. However, due to the strict time limits of product devel

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"Dual integral equations with $P^{m,n}_{-1/2+i\tau}({\rm ch}\alpha)$ and the weight function [1 + G(τ)]." In Generalized Associated Legendre Functions and Their Applications. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811783_0017.

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"Dual integral equations with the generalized Legendre function of the first kind $P^{m,n}_{-1/2+i\tau}({\rm ch}\alpha)$." In Generalized Associated Legendre Functions and Their Applications. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811783_0016.

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7

"Triple integral equations with the generalized Legendre function of the first kind $P^{m,n}_{-1/2+i\tau}({\rm ch}\alpha)$." In Generalized Associated Legendre Functions and Their Applications. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811783_0018.

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"The generalized associated Legendre functions." In Generalized Associated Legendre Functions and Their Applications. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811783_0002.

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9

"Relations between the generalized associated Legendre functions, Bessel functions, elliptic integrals and incomplete B-functions." In Generalized Associated Legendre Functions and Their Applications. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811783_0014.

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"Connection of the generalized associated Legendre functions with the Jacobi functions." In Generalized Associated Legendre Functions and Their Applications. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811783_0012.

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Conference papers on the topic "Generalized Legendre's associated function"

1

Yu, Ke, and David A. Peters. "Net Mass Flow Components in a Three-Dimensional Unsteady Rotor Inflow Model." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-42459.

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Potential flow equations are converted to ordinary differential equations by the Galerkin approach in which velocity and pressure potential functions are expanded in terms of closed-form solutions to Laplace’s Equation. The reduced number of generalized coordinates in a Galerkin approach gives advantages in real-time simulations, preliminary design, and dynamic eigenvalue analysis for aeroelasticity. Net mass injection from rotor sources is expected to occur in some situations, but cannot be treated by previous models. It is included in the present formulation. In this paper, frequency respons

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2

Shelake, Girish D., Sarika K. Nilapgol, and Priyanka D. Jirage. "Subclasses of univalent functions associated with generalized q-Mittag-Leffler function." In INTERNATIONAL CONFERENCE ON ADVANCES IN PURE & APPLIED MATHEMATICS (ICAPAM). AIP Publishing, 2025. https://doi.org/10.1063/5.0265526.

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Bhasin, Devesh, and Daniel A. McAdams. "Fostering Function-Sharing Using Bioinspired Product Architecture." In ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/detc2020-22580.

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Abstract In this work, we deduce principles of bioinspired product architectures to leverage biological function-sharing in engineering design. Function-sharing allows multiple functions to be performed by a single structure and can lead to improvements in cost, weight and other performance characteristics. Billions of years of evolution has led to the emergence of function-sharing adaptations in biological systems. However, the current practice of bioinspired function-sharing is largely limited to the solution-driven mimicry of biological structures. In order to effectively leverage biologica

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Choi, K. S., and J. Pan. "A Generalized Anisotropic Hardening Rule Based on the Mroz Multi-Yield-Surface Model." In ASME 2008 Pressure Vessels and Piping Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/pvp2008-61800.

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In this paper, a generalized anisotropic hardening rule based on the Mroz multi-yield-surface model is derived. The evolution equation for the active yield surface is obtained by considering the continuous expansion of the active yield surface during the unloading/reloading process. The incremental constitutive relation based on the associated flow rule is then derived for a general yield function. As a special case, detailed incremental constitutive relations are derived for the Mises yield function. The closed-form solutions for one-dimensional stress-plastic strain curves are also derived a

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Gururaja Rao, Lakshmi, and James T. Allison. "Generalized Viscoelastic Material Design With Integro-Differential Equations and Direct Optimal Control." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46768.

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Rheological material properties are examples of function-valued quantities that depend on frequency (linear viscoelasticity), input amplitude (nonlinear material behavior), or both. This dependence complicates the process of utilizing these systems in engineering design. In this article, we present a methodology to model and optimize design targets for such rheological material functions. We show that for linear viscoelastic systems simple engineering design assumptions can be relaxed from a conventional spring-dashpot model to a more general linear viscoelastic relaxation kernel, K(t). While

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Hong, In Seob, and Adrian Connolly. "Generalized Tolerance Limit Evaluation Method to Determine Statistically Meaningful Minimum Code Simulations." In 16th International Conference on Nuclear Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/icone16-48448.

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The tolerance limit approach has been internationally adopted for nuclear safety analyses as a way of identifying more realistic safety limits in the Best Estimate Plus Uncertainty (BEPU) methodology. The approach is based on the Wilks’ formula set suggested by the GRS (Gesellschaft fu¨r Anlagen-und Reaktorsicherheit), and consists of two approaches; one-sided approach to obtain a statistical meaning of the maximum output value in the multiple code runs, and two-sided approach for the minimum and maximum values at the same time. The Wilks’ formula set suggested by the GRS has been employed wit

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Lagoudas, Dimitris C., and Muhammad A. Qidwai. "Constitutive Modeling of 3-D Stress Induced Phase Transformation in Polycrystalline NiTi SMA." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0534.

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Abstract A thermomechanical description of the martenstitic phase transformation and the associated shape memory effect in polycrystalline NiTi shape memory alloys (SMAs) is presented. The Kuhn-Tucker optimality conditions, constraints on the evolution equations for transformation strain find the form of transformation function are obtained naturally through the principle of maximum transformation dissipation. Various transformation functions are investigated and a generalized Drucker-Prager type transformation function is proposed. Numerical results of the model based on different transformat

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Alecsa, Cristian Daniel. "G-KMM: A Flexible Kernel Mean Matching Optimization Method for Density Ratio Estimation Involving Multiple Train & Test Datasets." In 12th International Conference on Soft Computing, Artificial Intelligence and Applications. Academy & Industry Research Collaboration Center, 2023. http://dx.doi.org/10.5121/csit.2023.132422.

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In the present paper we introduce new optimization algorithms for the task of density ratio estimation. More precisely, we consider extending the well-known KMM (kernel mean matching) method using the construction of a suitable loss function, in order to encompass more general situations involving the estimation of density ratio with respect to subsets of the training data and test data, respectively. The codes associated to our Python implementation can be found at https://github.com/CDAlecsa/ Generalized-KMM.

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Bapat, Sushrut G., Ashok Midha, and Ashish B. Koli. "On a Generalized Approach for Design of Compliant Mechanisms Using the Pseudo-Rigid-Body Model Concept." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-38788.

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This paper provides a generalized approach for the design of compliant mechanisms. The paper discusses the implicit uncoupling, between the kinematic and energy/torque equations, enabled by the pseudo-rigid-body model concept, and utilizes it for designing a variety of compliant mechanism types for a wide-range of user specifications. Pseudo-rigid-body four-bar mechanisms, with one to four torsional springs located at the revolute joints, are considered to demonstrate the design methodology. Mechanisms are designed for conventional tasks, such as function, path and motion generation, and path

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Al-Ahdali, Issam, and David L. Shealy. "Optimization of three- and four-element lens systems by minimizing the caustic." In OSA Annual Meeting. Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.mz3.

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For an imaging optical system it is, in general, desirable to transform a collection of point sources of light into point images distributed over the focal plane with the appropriate magnification. In practice this is achieved by varying the lens system parameters such that the spread of a bundle of rays from each object point over the image plane has been minimized. A new generalized ray tracing program has been constructed to calculate the principal curvatures of the wavefront associated with a bundle of rays as it passes through an optical system. The caustic surfaces are formed by an optic

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Reports on the topic "Generalized Legendre's associated function"

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Rabbitt, Matthew P., and Matthew R. Beymer. Comparing food insecurity among the U.S. military and civilian adult populations. Economic Research Service, U.S. Department of Agriculture, 2024. http://dx.doi.org/10.32747/2024.8374828.ers.

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Readiness is a cornerstone of military service. Military readiness includes cognitive and physical abilities to train and execute missions. Previous studies among civilians demonstrate that food security is either directly or indirectly associated with cognitive function and body mass index. Therefore, food security is vital to maintaining military readiness. While no analyses have been conducted to date on the prevalence of food insecurity for a representative sample of the active duty U.S. military, studies of individual military installations have demonstrated food insecurity rates between

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