Categories
Tags
Special-functions
New post in Special-functions
Weber-type integral
October 11th, 2020
special-functions
error-function
integration
Interesting log sine integrals $\int_0^{\pi/3} \log^2 \left(2\sin \frac{x}{2} \right)dx= \frac{7\pi^3}{108}$
December 28th, 2020
definite-integrals
special-functions
integration
calculus
On Shanks' quartic approximation $\pi \approx \frac{6}{\sqrt{3502}}\ln(2u)$
June 20th, 2020
number-theory
special-functions
approximation
pi
Interesting integral related to the Omega Constant/Lambert W Function
September 8th, 2020
definite-integrals
special-functions
lambert-w
Solving Special Function Equations Using Lie Symmetries
February 28th, 2020
representation-theory
special-functions
ordinary-differential-equations
Why can't we define more elementary functions?
February 14th, 2020
elementary-functions
definition
special-functions
reference-request
Other interesting consequences of $d=163$?
August 1st, 2022
modular-forms
big-list
special-functions
algebraic-number-theory
number-theory
Is each of $\int_0^\infty\frac{dx}{x^x},\int_0^\infty\frac{dx}{x^{x^{x^x}}},\int_0^\infty\frac{dx}{x^{x^{x^{x^{x^x}}}}},\cdots$ less than $2$?
April 13th, 2022
integration
special-functions
power-towers
Integrate $\int_0^\pi\frac{3\cos x+\sqrt{8+\cos^2 x}}{\sin x}x\ \mathrm dx$
August 1st, 2022
closed-form
definite-integrals
special-functions
trigonometry
calculus
Non-trivial values of error function $\operatorname{erf}(x)$?
August 1st, 2022
special-functions
error-function
What is the role of mathematical intuition and common sense in questions of irrationality or transcendence of values of special functions?
May 9th, 2020
special-functions
gamma-function
irrational-numbers
philosophy
transcendental-numbers
Geometric & Intuitive Meaning of $SL(2,R)$, $SU(2)$, etc... & Representation Theory of Special Functions
August 1st, 2022
ordinary-differential-equations
representation-theory
special-functions
lie-groups
Why is Euler's Gamma function the "best" extension of the factorial function to the reals?
February 18th, 2022
education
gamma-function
special-functions
real-analysis
elliptic functions on the 17 wallpaper groups
February 26th, 2020
special-functions
symmetric-groups
elliptic-functions
tessellations
How to calculate hydrogenic radial wave functions?
August 1st, 2022
quantum-mechanics
software
physical-chemistry
wavefunction
special-functions
I want to solve Mathieu Equation $y''(x)+(a−2q \cos(2x))y(x)=0$. How to solve it using Floquet solution?
June 1st, 2020
quantum-optics
mathematical-physics
special-functions
Shift operator (integral calculus involving Hermite polynomials)
February 16th, 2020
special-functions
harmonic-oscillator
homework-and-exercises
quantum-mechanics
integration
Solving Special Function Equations Using Lie Symmetries
December 19th, 2020
differential-equations
lie-algebra
symmetry
mathematical-physics
special-functions
Complex energy eigenstates of the harmonic oscillator
May 17th, 2020
quantum-mechanics
harmonic-oscillator
special-functions
Frobenius’ Method to Solve an ODE (Hydrogen Atom - Radial Equation)
July 21st, 2020
ordinary-differential-equations
partial-differential-equations
quantum-groups
special-functions
Numerical approximation of the modified Bessel function $I_0$ with radical argument for integration purposes
August 1st, 2022
approximation
numerical-methods
integration
special-functions
Physical interpretation of the generating function for the Bessel functions.
May 13th, 2020
special-functions
physics
generating-functions
intuition
complex-analysis
Mean and variance of truncated generalized Beta distribution
August 4th, 2022
special-functions
probability
Product of two hypergeometric functions
November 28th, 2020
calculus
special-functions
hypergeometric-function
2-increasing functions
January 16th, 2020
special-functions
What is a mock theta function?
September 17th, 2020
special-functions
theta-functions
Vector Delta Function Identity
August 1st, 2022
dirac-delta
multivariable-calculus
special-functions
integration
Asymptotic expansion of integral involving modified Bessel-function
August 1st, 2022
special-functions
asymptotics
definite-integrals
Tables of Hypergeometric Functions
August 1st, 2022
reference-request
special-functions
Why is it that the Lambert W relation cannot be expressed in terms of elementary functions?
May 2nd, 2021
special-functions
lambert-w
elementary-functions
←
1
2
…
8
9
10
11
12
13
14
15
16
→