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When n is an integer >=0, then J_n(z) and J_(n+m)(z) have no common zeros other than at z=0 for m an integer >=1, where J_n(z) is a Bessel function of the first kind. The ...

A representation of a C^*-algebra A is a pair (H,phi) where H is a Hilbert space and phi:A->B(H) is a *-homomorphism. (H,phi) is said to be faithful if phi is injective. For ...

The Riemann sphere C^*=C union {infty}, also called the extended complex plane. The notation C^^ is sometimes also used (Krantz 1999, p. 82). The notation C^* is also used to ...

The field of complex numbers, denoted C.

If Omega_1 and Omega_2 are bounded domains, partialOmega_1, partialOmega_2 are Jordan curves, and phi:Omega_1->Omega_2 is a conformal mapping, then phi (respectively, ...

Let A be a unital Banach algebra. If a in A and ||1-a||<1, then a^(-1) can be represented by the series sum_(n=0)^(infty)(1-a)^n. This criterion for checking invertibility of ...

The antisymmetric parts of the Christoffel symbol of the second kind Gamma^lambda_(munu).

If P(x) is an irreducible cubic polynomial all of whose roots are real, then to obtain them by radicals, you must take roots of nonreal numbers at some point.

Special cases of general formulas due to Bessel. J_0(sqrt(z^2-y^2))=1/piint_0^pie^(ycostheta)cos(zsintheta)dtheta, where J_0(z) is a Bessel function of the first kind. Now, ...

For R[mu+nu]>1, int_(-pi/2)^(pi/2)cos^(mu+nu-2)thetae^(itheta(mu-nu+2xi))dtheta=(piGamma(mu+nu-1))/(2^(mu+nu-2)Gamma(mu+xi)Gamma(nu-xi)), where Gamma(z) is the gamma function.