Why exponentiation and power function with non-integer power are considered elementary functions while some other functions like Bernoulli polynomials generalized to non-integer order, polylogarithm, Hurwitz zeta and polygamma are not?
2026-04-08 15:44:52.1775663092
Why exponentiation is considered elementary funtion?
125 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in SPECIAL-FUNCTIONS
- Generalized Fresnel Integration: $\int_{0}^ {\infty } \sin(x^n) dx $ and $\int_{0}^ {\infty } \cos(x^n) dx $
- Is there any exponential function that can approximate $\frac{1}{x}$?
- What can be said about the series $\sum_{n=1}^{\infty} \left[ \frac{1}{n} - \frac{1}{\sqrt{ n^2 + x^2 }} \right]$
- Branch of Math That Links Indicator Function and Expressability in a Ring
- Generating function of the sequence $\binom{2n}{n}^3H_n$
- Deriving $\sin(\pi s)=\pi s\prod_{n=1}^\infty (1-\frac{s^2}{n^2})$ without Hadamard Factorization
- quotients of Dedekind eta at irrational points on the boundary
- Sources for specific identities of spherical Bessel functions and spherical harmonics
- Need better resources and explanation to the Weierstrass functions
- Dilogarithmic fashion: the case $(p,q)=(3,4)$ of $\int_{0}^{1}\frac{\text{Li}_p(x)\,\text{Li}_q(x)}{x^2}\,dx$
Related Questions in GAMMA-FUNCTION
- contour integral involving the Gamma function
- Generalized Fresnel Integration: $\int_{0}^ {\infty } \sin(x^n) dx $ and $\int_{0}^ {\infty } \cos(x^n) dx $
- Proving that $\int_{0}^{+\infty}e^{ix^n}\text{d}x=\Gamma\left(1+\frac{1}{n}\right)e^{i\pi/2n}$
- How get a good approximation of integrals involving the gamma function, exponentials and the fractional part?
- How to prove $\int_{0}^{\infty} \sqrt{x} J_{0}(x)dx = \sqrt{2} \frac{\Gamma(3/4)}{\Gamma(1/4)}$
- How do we know the Gamma function Γ(n) is ((n-1)!)?
- How to calculate this exponential integral?
- How bad is the trapezoid rule in the approximation of $ n! = \int_0^\infty x^n \, e^{-x} \, dx $?
- Deriving $\sin(\pi s)=\pi s\prod_{n=1}^\infty (1-\frac{s^2}{n^2})$ without Hadamard Factorization
- Find the value of $A+B+C$ in the following question?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?