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_2F_1(-1/2,-1/2;1;h^2) = sum_(n=0)^(infty)(1/2; n)^2h^(2n) (1) = 1+1/4h^2+1/(64)h^4+1/(256)h^6+... (2) (OEIS A056981 and A056982), where _2F_1(a,b;c;x) is a hypergeometric ...

Let f be an integer polynomial. The f can be factored into a product of two polynomials of lower degree with rational coefficients iff it can be factored into a product of ...

A geometric sequence is a sequence {a_k}, k=0, 1, ..., such that each term is given by a multiple r of the previous one. Another equivalent definition is that a sequence is ...

The identity PVint_(-infty)^inftyF(phi(x))dx=PVint_(-infty)^inftyF(x)dx (1) holds for any integrable function F(x) and phi(x) of the form ...

A group set is a set whose elements are acted on by a group. If the group G acts on the set S, then S is called a G-set. Let G be a group and let S be a G-set. Then for every ...

A ring that is commutative under multiplication, has a multiplicative identity element, and has no divisors of 0. The integers form an integral domain.

Let E be a set of expressions representing real, single-valued partially defined functions of one real variable. Let E^* be the set of functions represented by expressions in ...

A linear transformation of period two. Since a linear transformation has the form, lambda^'=(alphalambda+beta)/(gammalambda+delta), (1) applying the transformation a second ...

A parameterization is isothermal if, for zeta=u+iv and phi_k(zeta)=(partialx_k)/(partialu)-i(partialx_k)/(partialv), the identity phi_1^2(zeta)+phi_2^2(zeta)+phi_3^2(zeta)=0 ...

e^(izcostheta)=sum_(n=-infty)^inftyi^nJ_n(z)e^(intheta), where J_n(z) is a Bessel function of the first kind. The identity can also be written ...