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An even Walsh function with sequency k defined by Cal(n,k)=W(n,2k+1).

An odd Mathieu function se_r(z,q) with characteristic value a_r.

The relative rate of change of a function f(x) is the ratio if its derivative to itself, namely R(f(x))=(f^'(x))/(f(x)).

An odd Walsh function with sequency k defined by Sal(n,k)=W(n,2k).

The number of poles of an automorphic function in the closure of its fundamental region.

Solving the nome q for the parameter m gives m(q) = (theta_2^4(q))/(theta_3^4(q)) (1) = (16eta^8(1/2tau)eta^(16)(2tau))/(eta^(24)(tau)), (2) where theta_i(q)=theta_i(0,q) is ...

For a real positive t, the Riemann-Siegel Z function is defined by Z(t)=e^(itheta(t))zeta(1/2+it). (1) This function is sometimes also called the Hardy function or Hardy ...

The natural domain of a function is the maximal chain of domains on which it can be analytically continued to a single-valued function.

The variation of a function which exhibits slope changes, also called the saltus of a function. A series may also oscillate, causing it not to converge.

A harmonic number is a number of the form H_n=sum_(k=1)^n1/k (1) arising from truncation of the harmonic series. A harmonic number can be expressed analytically as ...