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searching for Euler's identity 8 found (60 total)

Homogeneous polynomial (955 words) [view diff] exact match in snippet view article find links to article

{d+n-1}{d}}={\frac {(d+n-1)!}{d!(n-1)!}}.} Homogeneous polynomial satisfy Euler's identity for homogeneous functions. That is, if P is a homogeneous polynomial

Integration using Euler's formula (905 words) [view diff] exact match in snippet view article find links to article

to use a half-angle formula to simplify the integrand. We can use Euler's identity instead: ∫cos2⁡xdx=∫(eix+e−ix2)2dx=14∫(e2ix+2+e−2ix)dx{\displaystyle

Sophomore's dream (1,315 words) [view diff] exact match in snippet view article find links to article

different domain (corresponding to changing variables by substitution), as Euler's identity itself can also be computed via an analogous integration by parts.

Trigonometric functions (8,994 words) [view diff] exact match in snippet view article find links to article

way that is similar to that of the above proof of Euler's identity. One can also use Euler's identity for expressing all trigonometric functions in terms

Polar coordinate system (6,214 words) [view diff] case mismatch in snippet view article find links to article

Cambridge University Press. ISBN 0-521-59461-8. Smith, Julius O. (2003). "Euler's Identity". Mathematics of the Discrete Fourier Transform (DFT). W3K Publishing

Discriminant (5,734 words) [view diff] exact match in snippet view article find links to article

partial derivative is not necessarily a zero of the polynomial (see Euler's identity for homogeneous polynomials). In the case of a homogeneous bivariate

Riemann zeta function (9,698 words) [view diff] exact match in snippet view article find links to article

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 fundamental

Generalized continued fraction (7,759 words) [view diff] exact match in snippet view article find links to article

convergence problem. Here are two continued fractions that can be built via Euler's identity. ex=x00!+x11!+x22!+x33!+x44!+⋯=1+x1−1x2+x−2x3+x−3x4+x−⋱{\displaystyle