Examples for

Representation Formulas

Oftentimes, mathematical expressions are not in the desired form for the purpose of their application. Representations are alternate forms of functions or expressions that make them easier to understand or use. Common representations are those that involve integrals, limits, infinite products or sums, power series, or representations through special functions. Wolfram|Alpha can find alternate representations of a specified form for a given mathematical function.
Integral Representations

Find representations of mathematical functions and expressions as integrals.

Find integral representations for a function:

log x integral representation
gamma(x) integral representation
Fresnel S(x) integral rep

Find representations satisfying given conditions:

integral representations of zeta(s) containing csch(t)
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Series Representations

Explore series representations of mathematical functions and expressions.

Find series representations for a function:

sin (pi x) series representations
zeta(s) series rep
Li(x) series rep

Find series representations for a number:

series rep. of pi^2/6
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Product Representations

Find product representations of a mathematical function or expression.

Find product representations for a function:

sin z product representation
zeta(s) product rep

Find product representations for a constant:

product rep. pi
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Limit Representations

Discover representations of functions and expressions as limits.

Find limit representations for a function:

exp(z) limit representation
Si(x) limit rep

Find limit representations for a constant:

limit representations of Euler gamma
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