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A sum which includes both the Jacobi triple product and the q-binomial theorem as special cases. Ramanujan's sum is ...

A conservative vector field (for which the curl del xF=0) may be assigned a scalar potential where int_CF·ds is a line integral.

A generalization of the Gaussian sum. For p and q of opposite parity (i.e., one is even and the other is odd), Schaar's identity states ...

A surface harmonic of degree l which is premultiplied by a factor r^l. Confusingly, solid harmonics are also known as "spherical harmonics" (Whittaker and Watson 1990, p. ...

F(x) = -Li_2(-x) (1) = int_0^x(ln(1+t))/tdt, (2) where Li_2(x) is the dilogarithm.

F(x) = Li_2(1-x) (1) = int_(1-x)^0(ln(1-t))/tdt, (2) where Li_2(x) is the dilogarithm.

A tensor defined in terms of the tensors which satisfy the double contraction relation.

A spheroidal harmonic is a special case of an ellipsoidal harmonic that satisfies the differential equation d/(dx)[(1-x^2)(dS)/(dx)]+(lambda-c^2x^2-(m^2)/(1-x^2))S=0 on the ...

A number taken to the power 2 is said to be squared, so x^2 is called "x squared." This terminology derives from the fact that the area of a square of edge length x is given ...

The squeeze theorem, also known as the squeezing theorem, pinching theorem, or sandwich theorem, may be stated as follows. Let there be two functions f_-(x) and f_+(x) such ...