The denominator of .
The generalized hypergeometric function of two variables (Kampe de Feriet function): .
The regularized generalized hypergeometric function of two variables (regularized Kampe de Feriet function): .
The Lauricella function A of variables: .
The Lauricella function B of variables: .
The Lauricella function C of variables: .
The Lauricella function D of variables: .
The Meijer G function: . The infinite contour of integration separates the poles of at , from the poles of at , . Such a contour always exists in the cases . There are three possibilities for the contour : (i) runs from γⅈ ∞ to γ+ⅈ ∞ (where ) so that all poles of , are to the left of , and all poles of , are to the right of ℒ. This contour can be a straight line if (then ). (In this case, the integral converges if , . If , then must be real and positive and the additional condition should be added.) (ii) is a left loop, starting and ending at ∞ and encircling all poles of ,, once in the positive direction, but none of the poles of , . In this case, the integral converges if and one of the following conditions is satisfied: ◼ or and ◼ and and and . (iii) is a right loop, starting and ending at +∞ and encircling all poles of , , once in the negative direction, but none of the poles of , . In this case, the integral converges if and one of the following conditions is satisfied: ◼ or and ◼ and and and . Identities containing MeijerG
The number of unrestricted partitions (independent of the order and with repetitions allowed) of the positive integer into a sum of strictly positive integers that add up to : . Identities containing PartitionsP
The prime number (the smallest integer greater than that cannot be divided by any integer greater than 1 and smaller than itself): . Identities containing Prime
A Boolean function that tests whether the angular momentum quantum numbers are physically realizable:
The number of ordered partitions (independent of the order and no repetitions allowed) of the positive integer into a sum of strictly positive integers which add up to : . Identities containing PartitionsQ
The Gauss type hypergeometric function :
The values of the Weierstrass zeta function at the halfperiods : .
The half‐periods for Weierstrass elliptic functions corresponding to the invariants :
The generalized Dirac comb function Ш(x): .
