mathematics, particularly p-adic analysis, the p-adic exponential function is a p-adic analogue of the usual exponential function on the complex numbers...

Mittag-Leffler function, a generalization of the exponential function p-adic exponential function Padé table for exponential function – Padé approximation...

In mathematics, p-adic analysis is a branch of number theory that studies functions of p-adic numbers. Along with the more classical fields of real and...

Marshall–Olkin exponential distribution Matrix exponential Moore's law Nachbin's theorem Piano key frequencies p-adic exponential function Power law Proof...

R), then the π-adic valuation and the π'-adic valuation are equal. Thus, the π-adic valuation can be called the P-adic valuation, where P = (π). The previous...

Legendre's formula that the p-adic exponential function has radius of convergence p − 1 / ( p − 1 ) {\displaystyle p^{-1/(p-1)}} . Legendre, A. M. (1830)...

(multi-valued) inverse function of the matrix exponential. Another example is the p-adic logarithm, the inverse function of the p-adic exponential. Both are defined...

trigintaduonions etc.) p-adic function: a function whose domain is p-adic. Linear function; also affine function. Convex function: line segment between...

e2πi = 1, in Cp, the field of p-adic complex numbers. p-adic exponential function Murty, M. Ram (2002). Introduction to P-Adic Analytic Number Theory. American...

2\right)2^{k}.} The function Q is a 2-adic isometry. Consequently, every infinite parity sequence occurs for exactly one 2-adic integer, so that almost...

the degree as a rational function and for total degree of the associated L-function for a toric exponential sum, using the p-adic method developed by Bombieri...

\mathbb {Q} } ⁠, one can define a p-adic Lie group over the p-adic numbers, a topological group which is also an analytic p-adic manifold, such that the group...

integer Mathematics portal Double exponential function – Exponential function of an exponential function Exponential decay – Decrease in value at a rate...

Pseudogamma function Hadamard's gamma function Inverse gamma function Lanczos approximation Multiple gamma function Multivariate gamma function p-adic gamma...

\mathbb {Q} } , such that | αi |p < 1/p for all i; then the p-adic exponentials expp(α1), . . . , expp(αn) are p-adic numbers that are algebraically independent...

the non-positive integers. In the p-adic numbers, it is not possible to continuously interpolate the factorial function directly, because the factorials...

between the Artin–Hasse exponential and the regular exponential in the spirit of the ergodic perspective (linking the p-adic and regular norms over the...

set of the p-adic numbers contains the rational numbers, but is not contained in the complex numbers. The elements of an algebraic function field over...

algebraic function with rational number coefficients. Through the theorem, it is readily demonstrable, for example, that the exponential function must be...

applications for matrix-valued geometric series, function-valued geometric series, p {\displaystyle p} -adic number geometric series, and most generally geometric...

_{p}=p^{-\nu _{p}(q)}} ⁠. Multiplying an integer by its ⁠ p {\displaystyle p} ⁠-adic absolute value cancels out the factors of ⁠ p {\displaystyle p} ⁠...

operators on the symmetric space G/K. For semisimple p-adic Lie groups, the theory of zonal spherical functions and Hecke algebras was first developed by Satake...

a subsystem of the 2-adic numbers as well as of the reals, and can represent the fractional parts of 2-adic numbers. Functions from natural numbers to...

on the ℓ-adic cohomology group Hi. The rationality of the zeta function follows immediately. The functional equation for the zeta function follows from...

other fields, such as fields of rational functions, algebraic function fields, algebraic number fields, and p-adic fields are commonly used and studied in...

be regarded as its norm.] However for another inverse function of the complex exponential function (and not the above defined principal value), the branch...

define the Theta functions over other fields where the exponential function might not be everywhere defined, such as fields of p-adic numbers. The Jacobi...

exponent. Define the p-adic valuation νp(n) to be the exponent of the highest power of the prime p that divides n. That is, if p is one of the pi then...

_{10}\left({\frac {d+1}{d}}\right)} . The tendency for real-world numbers to grow exponentially or logarithmically biases the distribution towards smaller leading digits...

{-\ln(1-z)}{1-z}},} where ln(z) is the natural logarithm. An exponential generating function is ∑ n = 1 ∞ z n n ! H n = e z ∑ k = 1 ∞ ( − 1 ) k − 1 k z...