We show how Rank-Crank type PDEs for higher order Appell functions due to Zwegers may be obtained from a generalized Lambert series identity due to the first author. Special cases are the Rank-Crank PDE due to Atkin and the third author and a PDE for a level 5 Appell function also found by the third author. These two special PDEs are related to generalized Lambert series identities due to Watso...

We use a generalized Lambert series identity due to the first author to present qseries proofs of recent results of Imamoğlu, Raum and Richter concerning recursive formulas for the coefficients of two 3rd order mock theta functions. Additionally, we discuss an application of this identity to other mock theta functions.

Abstract. The purpose of this paper is to consider a new generalization of the Hurwitz zeta function. Generating functions, Mellin transform, and a series identity are obtained for this generalized class of functions. Some of the results are used to provide a further generalization of the Lambert transform. Relevance with various known results are depicted invariably. Multivariable extensions a...

Seo and others have generalized an identity of Postnikov by finding expressions for the generating function for the number of proper vertices in certain families of rooted trees and forests. We describe an approach to these results that involves a straightforward inductive argument and a version of the Lambert-Rothe identities.

Modern Logic, forthcoming. 9. K. Lambert, editor. Philosophical Applications of Free Logic. Oxford University Press, Oxford, 1991. 10. Karel Lambert. Nonextensionality. In W. Lenzen, editor, Festschrift fur Franz von Kutschera. de Gruyter, Berlin, 1997. 11. Karel Lambert and Bas van Fraassen. Derivation and Counterexample: An Introduction to Philosophical Logic. Dickenson, Encino, CA, 1972. 12...

We revisit old conjectures of Fermat and Euler regarding representation of integers by binary quadratic form x2 + 5y2. Making use of Ramanujan’s 1ψ1 summation formula we establish a new Lambert series identity for ∑∞ n,m=−∞ q n2+5m2 . Conjectures of Fermat and Euler are shown to follow easily from this new formula. But we don’t stop there. Employing various formulas found in Ramanujan’s noteboo...

Despite overall psychotherapy efficacy (Lambert, 2013), many clients do not benefit (Reese, Duncan, Bohanske, Owen, & Minami, 2014), dropouts are a problem (Swift & Greenberg, 2012), and therapists vary significantly in success rates (Baldwin & Imel, 2013), are poor judges of negative outcomes (Chapman et al., 2012), and grossly overestimate their effectiveness (Walfish, McAlister, O'Donnell, &...

M2-branes can blow up into BPS funnels that end on calibrated intersections of M5-branes. In this quick note, we make the observation that the constraints required for the consistency of these solutions are automatic in Bagger-Lambert-Gustavsson (BLG) theory, thanks to the fundamental identity and the supersymmetry of the calibration. We also explain how the previous ad hoc fuzzy funnel constru...

We study tensor products of two structures situated, in a sense, between normed spaces and (abstract) operator spaces. We call them Lambert and proto-Lambert spaces and pay more attention to the latter ones. The considered two tensor products lead to essentially different norms in the respective spaces. Moreover, the proto-Lambert tensor product is especially nice for spaces with the maximal pr...

A procedure for deriving analytic partial derivatives of the Lambert problem is presented. Using the universal, cosine based Lambert formulation; first order partial derivatives of the velocities with respect to the positions and times are developed. Taking advantage of inherent symmetries and intermediate variables, the derivatives are expressed in a computationally efficient form. The added c...