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What (who) is cylindrical integral - definition

MAP PROJECTION

Miller projection; Miller cylindrical; Miller Cylindrical; World Miller Cylindrical; Miller cylindrical map projection

Henstock–Kurzweil integral

GENERALIZATION OF THE RIEMANN INTEGRAL

Henstock-Kurzweil Integral; Perron integral; Gauge integral; Henstock integral; Denjoy Integral; Henstock-Kurzweil-Stieltjes integral; Perron Integral; Henstock-Kurzweil-Stieltjes Integral; Generalized Riemann integral; Denjoy-Perron integral; Henstock-Kurzweil integral; H-K integral

In mathematics, the Henstock–Kurzweil integral or generalized Riemann integral or gauge integral – also known as the (narrow) Denjoy integral (pronounced ), Luzin integral or Perron integral, but not to be confused with the more general wide Denjoy integral – is one of a number of inequivalent definitions of the integral of a function. It is a generalization of the Riemann integral, and in some situations is more general than the Lebesgue integral.

https://en.wikipedia.org/wiki/Henstock–Kurzweil_integral

Pettis integral

Weak integral; Gelfand-Pettis integral; Gelfand–Pettis integral; Gelfand integral; Dunford integral

In mathematics, the Pettis integral or Gelfand–Pettis integral, named after Israel M. Gelfand and Billy James Pettis, extends the definition of the Lebesgue integral to vector-valued functions on a measure space, by exploiting duality.

https://en.wikipedia.org/wiki/Pettis_integral

Improper integral

$The improper integral<br/><math>\int_{0}^{\infty} \frac{dx}{(x+1)\sqrt{x}} = \pi</math><br/> has unbounded intervals for both domain and range.$
$The improper integral<br/><math>\int_{-1}^{1} \frac{dx}{\sqrt[3]{x^2}} = 6</math><br/> converges, since both left and right limits exist, though the integrand is unbounded near an interior point.$

LIMIT OF A DEFINITE INTEGRAL WITH AS ONE OR BOTH LIMITS APPROACH INFINITY OR VALUES AT WHICH THE INTEGRAND IS UNDEFINED

Improper Riemann integral; Improper integrals; Improper Integrals; Proper integral

In mathematical analysis, an improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number or positive or negative infinity; or in some instances as both endpoints approach limits. Such an integral is often written symbolically just like a standard definite integral, in some cases with infinity as a limit of integration.

https://en.wikipedia.org/wiki/Improper_integral

Wikipedia

Miller cylindrical projection

The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of 4⁄5, projected according to Mercator, and then the result is multiplied by 5⁄4 to retain scale along the equator. Hence:

or inversely,

where λ is the longitude from the central meridian of the projection, and φ is the latitude. Meridians are thus about 0.733 the length of the equator.

In GIS applications, this projection is known as: "ESRI:54003 – World Miller Cylindrical".

Compact Miller projection is similar to Miller but spacing between parallels stops growing after 55 degrees.

https://en.wikipedia.org/wiki/Miller cylindrical projection