In this paper we derive the explicit, closed-form, recursion-free formulae for the arbitrary-order Fréchet derivatives of the exponential and logarithmic functions in unital Banach algebras (complex ...

Figure 2 Although the Gaussian function is similar to the Exponential function, it leads to less line broadening than the Exponential function. Figure 3 Optimizing the Spectrum In general, optimal ...

James Berger, Improving on Inadmissible Estimators in Continuous Exponential Families with Applications to Simultaneous Estimation of Gamma Scale Parameters, The Annals of Statistics, Vol. 8, No. 3 ...

Prolate spheroidal wave functions (PSWFs) and their discrete counterparts – the discrete prolate spheroidal sequences (DPSSs) – have emerged as essential tools in the analysis of band ...

In everyday speech, exponential growth means runaway expansion. Math class taught us that compound interest, population increase, or radioactive decay are all applications of exponential functions ...

Prolate Spheroidal Wave Functions (PSWFs): Special functions optimised for representing band‐limited signals, providing an orthogonal basis with excellent time–frequency localisation.