Leibniz rules and reality conditions

G. Fiore; J. Madore

doi:10.1007/s100520000470

Duality on the quantum space(3) with two parameters

Open Physics ◽

10.2478/s11534-012-0092-1 ◽

2012 ◽

Vol 10 (5) ◽

Author(s):

Muttalip Özavşar ◽

Gürsel Yeşilot

Keyword(s):

Hopf Algebra ◽

Lie Algebra ◽

Differential Forms ◽

Quantum Space ◽

Dual Algebra ◽

Commutation Relations ◽

Dual Hopf Algebra ◽

Invariant Differential ◽

Leibniz Rules ◽

Two Parameters

AbstractIn this study, we introduce a dual Hopf algebra in the sense of Sudbery for the quantum space(3) whose coordinates satisfy the commutation relations with two parameters and we show that the dual algebra is isomorphic to the quantum Lie algebra corresponding to the Cartan-Maurer right invariant differential forms on the quantum space(3). We also observe that the quantum Lie algebra generators are commutative as those of the undeformed Lie algebra and the deformation becomes apparent when one studies the Leibniz rules for the generators.

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Leibniz rules for multivariate divided differences

Journal of Approximation Theory ◽

10.1016/j.jat.2014.02.002 ◽

2014 ◽

Vol 181 ◽

pp. 43-53 ◽

Cited By ~ 1

Author(s):

Jesús Carnicer ◽

Tomas Sauer

Keyword(s):

Divided Differences ◽

Leibniz Rules

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G. H. R. Parkinson. Introduction. Leibniz, Logical papers, A selection translated and edited with an introduction by G. H. R. Parkinson, Clarendon Press, Oxford1966, pp. ix–Ixv. - Gottfried Wilhelm Leibniz. From Of the art of combination (1666). English translation of a portion of 11 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 1–11. - Gottfried Wilhelm Leibniz. Elements of a calculus (April, 1679). English translation of 114 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 17–24. - Gottfried Wilhelm Leibniz. Rules from which a decision can be made, by means of numbers, about the validity of inferences and about the forms and moods of categorical syllogisms (April, 1679). English translation of 118 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 25–32. - Gottfried Wilhelm Leibniz. A specimen of the universal calculus (1679–86?). English translation of 111 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 33–39. - Gottfried Wilhelm Leibniz. Addenda to the specimen of the universal calculus (1679–86?). English translation of 111 (without the three concluding paragraphs from Couturat) by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 40–46. - Gottfried Wilhelm Leibniz. General inquiries about the analysis of concepts and of truths (1686). English translation of 129 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 47–87. - Gottfried Wilhelm Leibniz. The primary bases of a logical calculus (1 August 1690). English translation of 133 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 90–92. - Gottfried Wilhelm Leibniz. The bases of a logical calculus (2 August 1690). English translation of 134 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 93–94. - Gottfried Wilhelm Leibniz. An intensional account of immediate inference and the syllogism (‘Logical definitions’). English translation of 18 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 112–114. - Gottfried Wilhelm Leibniz. A paper on ‘some logical difficulties’ (after 1690). English translation of 13 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 115–121. - Gottfried Wilhelm Leibniz. A study in the plus-minus calculus (‘A not inelegant specimen of abstract proof’) (after 1690). English translation of 16 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 122–130. - Gottfried Wilhelm Leibniz. A study in the calculus of real addition (after 1690). English translation of 112 by G. H. R. Parkinson. Clarendon Press, Oxford1966, pp. 131–144.

Journal of Symbolic Logic ◽

10.2307/2270116 ◽

1968 ◽

Vol 33 (1) ◽

pp. 139-140

Author(s):

Alonzo Church

Keyword(s):

English Translation ◽

Gottfried Wilhelm Leibniz ◽

Logical Calculus ◽

Real Addition ◽

Leibniz Rules

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New Expansion Formulas for a Family of theλ-Generalized Hurwitz-Lerch Zeta Functions

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2014/131067 ◽

2014 ◽

Vol 2014 ◽

pp. 1-13 ◽

Cited By ~ 7

Author(s):

H. M. Srivastava ◽

Sébastien Gaboury

Keyword(s):

Fractional Calculus ◽

Zeta Functions ◽

Chain Rule ◽

New Family ◽

Special Cases ◽

Leibniz Rules

We derive several new expansion formulas for a new family of theλ-generalized Hurwitz-Lerch zeta functions which were introduced by Srivastava (2014). These expansion formulas are obtained by making use of some important fractional calculus theorems such as the generalized Leibniz rules, the Taylor-like expansions in terms of different functions, and the generalized chain rule. Several (known or new) special cases are also considered.

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New Relations Involving an Extended Multiparameter Hurwitz-Lerch Zeta Function with Applications

International Journal of Analysis ◽

10.1155/2014/680850 ◽

2014 ◽

Vol 2014 ◽

pp. 1-14 ◽

Cited By ~ 5

Author(s):

H. M. Srivastava ◽

Sébastien Gaboury ◽

Richard Tremblay

Keyword(s):

Fractional Calculus ◽

Zeta Function ◽

Chain Rule ◽

Special Cases ◽

Lerch Zeta Function ◽

Leibniz Rules

We derive several new expansion formulas involving an extended multiparameter Hurwitz-Lerch zeta function introduced and studied recently by Srivastava et al. (2011). These expansions are obtained by using some fractional calculus methods such as the generalized Leibniz rules, the Taylor-like expansions in terms of different functions, and the generalized chain rule. Several (known or new) special cases are also given.

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