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_8phi_7[a,qa^(1/2),-qa^(1/2),b,c,d,e,q^(-N); a^(1/2),-a^(1/2),(aq)/b,(aq)/c,(aq)/d,(aq)/e,aq^(N+1);q,(aq^(N+2))/(bcde)] ...

Let y_n be a complex number for 1<=n<=N and let y_n=0 if n<1 or n>N. Then (Montgomery 2001).

The system of partial differential equations del ^4u = E(v_(xy)^2-v_(xx)v_(yy)) (1) del ^4v = alpha+beta(u_(yy)v_(xx)+u_(xx)v_(yy)-2u_(xy)v_(xy)), (2) where del ^4 is the ...

There are several commonly used methods of defining the slippery, but extremely important, concept of a continuous function (which, depending on context, may also be called a ...

The Riemann integral is the definite integral normally encountered in calculus texts and used by physicists and engineers. Other types of integrals exist (e.g., the Lebesgue ...

A singular point of an algebraic curve is a point where the curve has "nasty" behavior such as a cusp or a point of self-intersection (when the underlying field K is taken as ...

The operator D=-i(d+d^*), where d^* is the adjoint.

A dual bivector is defined by X^~_(ab)=1/2epsilon_(abcd)X^(cd), and a self-dual bivector by X_(ab)^*=X_(ab)+iX^~_(ab).

Can be used to invert a Laplace transform.

sum_(i=1)^n((partialu)/(partialx_i))^2=1.