- }t^{z-1}\,\mathrm {e} ^{-t}\,dt} For
positive integers m and n, the two
integrals can be
expressed in
terms of
factorials and
binomial coefficients: B(n...
- contributions.
Eulerian integrals were
first studied by
Euler and
afterwards investigated by Legendre, by whom they were
classed as
Eulerian integrals of the...
- constant. The
Euler substitutions for
integrals involving a
square root. Euler's
summation formula, a
theorem about integrals. Cauchy–Euler
equation (or Euler...
- The
double integrals are
surface integrals over the
surface Σ, and the line
integral is over the
bounding curve ∂Σ. The
Leibniz integral rule can be...
- }^{x}{\frac {dt}{\ln t}}\right).} The
offset logarithmic integral or
Eulerian logarithmic integral is
defined as Li(x)=∫2xdtlnt=li(x)−li(2).{\displaystyle...
-
titled Über die
Theorie der
Eulerschen Integrale ("On the
Theory of
Eulerian integrals"). This
thesis did not
display the
talent evident in Dedekind's subsequent...
-
closed form of
integrals of the Fermi–Dirac
distribution and the Bose–Einstein distribution, and is also
known as the Fermi–Dirac
integral or the Bose–Einstein...
-
David H.; Borwein, David; Borwein,
Jonathan M. (2015). "On
Eulerian log-gamma
integrals and Tornheim-Witten zeta functions". The
Ramanujan Journal. 36...
- (t-1)^{5}(t+2)^{4}(t-3)},
making it an
integral graph—a
graph whose spectrum consists entirely of integers. An
Eulerian subgraph of a
graph G{\displaystyle...
- (x-6)(x-2)^{6}(x+2)^{9}}. Therefore, the
Shrikhande graph is an
integral graph: its
spectrum consists entirely of integers. It has book thickness...
