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Externally erect a square on the side BC. Now join the new vertices S_(AB) and S_AC of this square with the vertex A, marking the points of intersection Q_(A,BC) and ...

A triangle DeltaA^'B^'C^' is said to be inscribed in a triangle DeltaABC if A^' lies on BC, B^' lies on CA, and C^' lies on AB (Kimberling 1998, p. 184). Examples include the ...

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 ...

The circumcircle of the Johnson triangle DeltaJ_AJ_BJ_C has center at the orthocenter H of the reference triangle and radius R, where R is the circumradius of the reference ...

Applying the Kaprekar routine to 4-digit number reaches 0 for exactly 77 4-digit numbers, while the remainder give 6174 in at most 8 iterations. The value 6174 is sometimes ...

The infinite product identity Gamma(1+v)=2^(2v)product_(m=1)^infty[pi^(-1/2)Gamma(1/2+2^(-m)v)], where Gamma(x) is the gamma function.

Let J_nu(z) be a Bessel function of the first kind, N_nu(z) a Bessel function of the second kind, and j_(nu,n)(z) the zeros of z^(-nu)J_nu(z) in order of ascending real part. ...

The symbol defined by c^(a/b) = c(c+b)(c+2b)...[c+(a-1)b] (1) = b^a(c/b)_a (2) = (b^aGamma(a+c/b))/(Gamma(c/b)), (3) where (a)_n is the Pochhammer symbol and Gamma(z) is the ...

A transformation of a hypergeometric function,

An identity which relates hypergeometric functions,