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Expanding the Riemann zeta function about z=1 gives zeta(z)=1/(z-1)+sum_(n=0)^infty((-1)^n)/(n!)gamma_n(z-1)^n (1) (Havil 2003, p. 118), where the constants ...

A hyperbola (plural "hyperbolas"; Gray 1997, p. 45) is a conic section defined as the locus of all points P in the plane the difference of whose distances r_1=F_1P and ...

A parabola (plural "parabolas"; Gray 1997, p. 45) is the set of all points in the plane equidistant from a given line L (the conic section directrix) and a given point F not ...

How can a delegation of six regiments, each of which sends a colonel, a lieutenant-colonel, a major, a captain, a lieutenant, and a sub-lieutenant be arranged in a regular ...

Given a Taylor series f(z)=sum_(n=0)^inftyC_nz^n=sum_(n=0)^inftyC_nr^ne^(intheta), (1) where the complex number z has been written in the polar form z=re^(itheta), examine ...

A quantity such as a polynomial discriminant which remains unchanged under a given class of algebraic transformations. Such invariants were originally called ...

Given a ship with a known constant direction and speed v, what course should be taken by a chase ship in pursuit (traveling at speed V) in order to intercept the other ship ...

Enclose a sphere in a cylinder and cut out a spherical segment by slicing twice perpendicularly to the cylinder's axis. Then the lateral surface area of the spherical segment ...

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

A Bäcklund transformation allows additional solutions to a nonlinear partial differential equations to be found if one particular solution is already known.