📈 So you thought you could dodge #calculus with a “conceptual” take on Euler's formula? 😂 Spoiler: it's just a fancy way to say you're still drowning in power series, but now with extra philosophy! 🧠🔄
http://www.deaneyang.com//blog/blog/math/exponential-function/euler-formula/2025/05/29/ExponentialFunctions.html #PowerSeries #Humor #MathPhilosophy #DrowningInMath #HackerNews #ngated

Honor Unveils Power Lineup: Mid-Range Phones With Large 8,000mAh Batteries

#batterylife #honor #MidRangePhones #PowerSeries #smartphone
https://blazetrends.com/honor-unveils-power-lineup-mid-range-phones-with-large-8000mah-batteries/?fsp_sid=6638

more curves and polynomials

https://bugfreeblog.duckdns.org/2021/05/isogeometric-analysis-bezier-curves-and.html

#powerseries

The integral

\[ \int_0^\infty x^k e^{-x} dx = k! \]

is used as motivation for the gamma function and in the irrationality proof of \( e \). But it can also be used for the transformation \( T \) defined by

\[ T f = \int_0^\infty f(x) e^{-x} dx. \]

If \( f = \sum_i f_i x^i \) is a power series and everything converges, it is transformed to \( T f = \sum_i f_i i! \). One can therefore say that \( T \) evaluates \( f \) at the factorial and write

\[ T f = f(!). \]

Are there other unusual places at which one can evaluate a function?

#Mathematics #PowerSeries #Integrals

Two must reads for anyone serious about sequences, computing methodologies, and combinatorial algorithms.

S. Yurkevich, The art of algorithmic guessing in gfun,
https://doi.org/10.5206/mt.v2i1.14421

B. T. Tabuguia, W. Koepf, On the Rep. of Non-Holonomic Univariate Power Series,
https://doi.org/10.5206/mt.v2i1.14315

The examples are primarily aimed at Maple users but the expositions are general enough to give a good start.

#TheArtOfGuessing, #P-recursive sequences, #D-finite functions, #Holonomic, #PowerSeries

For an insurance company to be successful over T, earning >claim , e> c
What premium { q} over T
-> {C=\Sigma X_{i}} < Nq} This large deviations theory i.i.d. random variables, where rate function is expressed as a #powerseries

For an insurance company to be successful over T, earning >claim , e> c
What premium { q} over T
-> {C=\Sigma X_{i}} < Nq} This large deviations theory i.i.d. random variables, where rate function is expressed as a #powerseries

complex analytic function is defined in an open ball B around a point x_0, its #powerseries expansion at x_0 is convergent in whole open ball (holomorphic functions are analytic) (1)
For real analytic functions (B : open interval of real line r/t an open disk of complex plane)

complex analytic function is defined in an open ball B around a point x_0, its #powerseries expansion at x_0 is convergent in whole open ball (holomorphic functions are analytic) (1)
For real analytic functions (B : open interval of real line r/t an open disk of complex plane)