In mathematics, a reflection formula or reflection relation for a function f is a relationship between f(a − x) and f(x). It is a special case of a functional...

example: the reflection formula essentially represents the sine function as the product of two gamma functions. Starting from this formula, the exponential...

n+{\frac {1}{8n}}}}\right)\qquad n\geq 1} which both spring off the reflection formula via 0 = ψ ( 1 − x n ) = ψ ( x n ) + π tan ⁡ π x n {\displaystyle 0=\psi...

The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident...

equation for the gamma function, can be used to obtain the following reflection formula for the Barnes G-function (originally proved by Hermann Kinkelin):...

reflection, a reflection across a point Reflection (mathematics), a transformation of a space Reflection formula, a relation in a function Reflective subcategory...

of Coxeter groups. Reflection across an arbitrary line through the origin in two dimensions can be described by the following formula Ref l ⁡ ( v ) = 2...

_{j=1}^{n}{\frac {H_{j,c}}{(j+1)^{b}}}} The above MZVs satisfy the Euler reflection formula: ζ ( a , b ) + ζ ( b , a ) = ζ ( a ) ζ ( b ) − ζ ( a + b ) {\displaystyle...

in three dimensions Euler's reflection formula, reflection formula for the gamma function Local Euler characteristic formula The Euler function, a modular...

(r/|D|)^{\chi (r){\frac {w}{2h}}}} for some algebraic number α. Using Euler's reflection formula for the gamma function gives: η ( i ) = 2 − 1 π − 3 / 4 Γ ( 1 4 )...

Both sides of the Euler product formula converge for Re(s) > 1. The proof of Euler's identity uses only the formula for the geometric series and the...

formula as stated here is only valid for arguments in the right complex half-plane, it can be extended to the entire complex plane by the reflection formula...

factorial. In particular, and by means of the reflection formula, In analogy with the half-integer formula, Γ ( n + 1 3 ) = Γ ( 1 3 ) ( 3 n − 2 ) ! ! !...

(z\not \in ~]-\infty ;0]),} and applying the reflection formula to each dilogarithm we find the inversion formula Li 2 ⁡ ( z ) + Li 2 ⁡ ( 1 / z ) = − 1 6 π...

m ) = m g m ( n ) {\displaystyle ng_{n}(m)=mg_{m}(n)} , a kind of reflection formula), and M n ( x ) = ( n − 1 ) ! ∑ k = 1 n k 2 k ( n k ) ( x k ) {\displaystyle...

Unigrafia, p. 27, ISBN 978-951-51-8695-9, ISSN 2814-4031 "Euler's Reflection Formula - ProofWiki", proofwiki.org, retrieved 2020-09-02 Paris, R. B. (2010)...

results in her report on "Some Conclusions Derived from the Fresnel Reflection Formula". In 1906, while engaged in this research, Meitner was introduced...

principle that the angle of reflection of light from a surface is the same as the angle of incidence Reflection formula, a relation between f(x) and...

In physics, total internal reflection (TIR) is the phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from...

{\displaystyle f(z)f(1-z)={\pi \over \sin(\pi z)}}           (Euler's reflection formula) The functional equation f ( a z + b c z + d ) = ( c z + d ) k f (...

{Li} _{2}(1-z)={\frac {{\pi }^{2}}{6}}-\ln z\cdot \ln(1-z).} The reflection formula. Li 2 ⁡ ( − z ) − Li 2 ⁡ ( 1 − z ) + 1 2 Li 2 ⁡ ( 1 − z 2 ) = − π...

Euler's reflection formula Γ ( z ) Γ ( 1 − z ) = π sin ⁡ π z . {\displaystyle \Gamma (z)\Gamma (1-z)={\frac {\pi }{\sin \pi z}}.} However, this formula cannot...

One of the most common reflection principles for ZFC is a theorem schema that can be described as follows: for any formula ϕ ( x 1 , … , x n ) {\displaystyle...

{x^{2}}{n^{2}}}\right)} and is related to the gamma function Γ(x) through Euler's reflection formula: sin ⁡ ( π x ) π x = 1 Γ ( 1 + x ) Γ ( 1 − x ) . {\displaystyle {\frac...

Specular reflection, or regular reflection, is the mirror-like reflection of waves, such as light, from a surface. The law of reflection states that a...

{2}}}{{\sqrt {3}}+1}}\right)} In general, from the Barnes G-function reflection formula, Cl 2 ⁡ ( 2 π z ) = 2 π log ⁡ ( G ( 1 − z ) G ( z ) ) − 2 π log ⁡...

{\displaystyle \Gamma (s)} is the gamma function. The functional equation (or reflection formula) for Landau's   ξ   {\displaystyle ~\xi ~} is ξ ( 1 − s ) = ξ ( s...

-\theta }{2}}} . With the help of a trigonometric identity known as a reflection formula, the relationship between θ and b can be resolved to:: 673  r min...

{z}})} gives the duplication formula, z − 1 / 2 J 1 ( z ) {\textstyle z^{-1/2}J_{1}({\sqrt {z}})} gives the reflection formula, and fixing to the evaluable...

q+{\frac {n}{k}}\right).} The periodic zeta function occurs in the reflection formula for the Hurwitz zeta function, which is why the relation that it obeys...