Is there any $x\in(0,1)\cap\mathbb Q$ different from $1/2$ such that $\Gamma(x)$ is algebraic over $\mathbb Q(\pi)$?
2026-03-28 00:44:18.1774658658
Algebraic values of the Gamma function using $\pi$
60 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in COMPLEX-ANALYSIS
- Minkowski functional of balanced domain with smooth boundary
- limit points at infinity
- conformal mapping and rational function
- orientation of circle in complex plane
- If $u+v = \frac{2 \sin 2x}{e^{2y}+e^{-2y}-2 \cos 2x}$ then find corresponding analytical function $f(z)=u+iv$
- Is there a trigonometric identity that implies the Riemann Hypothesis?
- order of zero of modular form from it's expansion at infinity
- How to get to $\frac{1}{2\pi i} \oint_C \frac{f'(z)}{f(z)} \, dz =n_0-n_p$ from Cauchy's residue theorem?
- If $g(z)$ is analytic function, and $g(z)=O(|z|)$ and g(z) is never zero then show that g(z) is constant.
- Radius of convergence of Taylor series of a function of real variable
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?
Related Questions in TRANSCENDENTAL-NUMBERS
- Two minor questions about a transcendental number over $\Bbb Q$
- Is it possible to express $\pi$ as $a^b$ for $a$ and $b$ non-transcendental numbers?
- Is it true that evaluating a polynomial with integer coefficients at $e$, uniquely defines it?
- Is $\frac{5\pi}{6}$ a transcendental or an algebraic number?
- Is there any intermediate fields between these two fields？
- Is there any pair of positive integers $ (x,n)$ for which :$e^{{e}^{{e}^{\cdots x}}}=2^{n}$?
- Why is :$\displaystyle {e}^\sqrt{2}$ is known to be transcedental number but ${\sqrt{2}}^ {e}$ is not known?
- Irrationality of $\int_{-a}^ax^nn^xd x$
- Proving that $ 7<\frac{5\phi e}{\pi}< 7.0000689$ where $\phi$ is the Golden Ratio
- Transcendence of algebraic numbers with Transcendental power
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?