
The natural boundary of analyticity of the function with respect to is the set boundary.

Gives a list of lists of the branch points (if present, including infinity) of the function f over the complex ‐plane.

The ramification index for function in the branch point .

The set of poles (with their orders) and essential singularities of with respect to . (The order of essential singularity is ∞.)

The list of the (parametrized) intervals where the function is discontinuous over the complex ‐plane.

Asymptotic relation that reflects the boundedness of near point .

Asymptotic relation that reflects the boundedness of near point .

The asymptotic expansion of the function at the point that includes terms of the asymptotic expansions of the regular and exponential components: .
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Sum of terms excluding the term .

Limit of the finite sum (infinite sum): .

Limit of the finite sum (infinite sum): .

Sum over all solutions of the equation .

Sum over the set .

Sum of over all divisors of n.

Multiple sum of function over the sets .

Limit of finite product .

Product over set .

Product of over all divisors of n.

Indefinite integral (antiderivative) of function . Inverse operation to differentiation: .

Multiple definite integral of the function by the intervals .

Cauchy principal value of a singular integral:  Cauchy principal value of a singular integral: 

The special contour , which is used in the definition of the Meijer G function and its numerous particular cases. There are three possibilities for the contour : (i) runs from γ-ⅈ ∞ to γ+ⅈ ∞ (where ) so that all poles of , are to the left of ℒ, and all poles of , , are to the right.
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 loop on the left side of the complex plane, starting and ending at -∞ and encircling all poles of , , once in the clockwise direction, but none of the poles of , .
(In this case, the integral converges if and either , or and , or and and both and .) (iii) is a loop on the right side of the complex plane, starting and ending at +∞ and encircling all poles of , , once in the counterclockwise direction, but none of the poles of , .
(In this case, the integral converges if and either , or and , or and and both and .)

Wigner integral transform: . (If this integral does not converge, the value of is defined in the sense of generalized functions.)

A finite continued fraction 

Limit of the finite continued fraction .

The matrix with elements .

The determinant of the matrix with elements .
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