## Abstract

With the use of rectangular coordinates O-XYZ, the potential of a calculation point P is expressed in the form of a triple repeated integral of a density {sigma} at point Q in the mass. The potential at the density {sigma} assumed to be 1 is named the potential of a polygonal prism. Further, a double repeated integral with an integral concerning Z removed from the triple integral is named the potential of polygonal lamina. This potential can be expressed in a quadratic form (linear form) with 2nd order partial derivative (1st order partial derivative) as a coefficient. On the contrary, in order to extract the 1st/2nd order partial derivatives from this potential by partial differential, it requires partial differentiation with these partial derivatives considered to be a constant. The reason that they can be realized is attributable to the zero result of the linear form which has as the coefficient a 3rd order partial derivative concerning the variable of integration in a primitive function. If this relation is used, the integral calculation and description may be simplified. An explanation was given with examples enumerated so that these conditions might be understood.

## Citation Formats

Koyama, S.
Potential of a polygonal prism and lamina; Takakuchu men no potential.
Japan: N. p.,
1996.
Web.

Koyama, S.
Potential of a polygonal prism and lamina; Takakuchu men no potential.
Japan.

Koyama, S.
1996.
"Potential of a polygonal prism and lamina; Takakuchu men no potential."
Japan.

@misc{etde_395540,

title = {Potential of a polygonal prism and lamina; Takakuchu men no potential}

author = {Koyama, S}

abstractNote = {With the use of rectangular coordinates O-XYZ, the potential of a calculation point P is expressed in the form of a triple repeated integral of a density {sigma} at point Q in the mass. The potential at the density {sigma} assumed to be 1 is named the potential of a polygonal prism. Further, a double repeated integral with an integral concerning Z removed from the triple integral is named the potential of polygonal lamina. This potential can be expressed in a quadratic form (linear form) with 2nd order partial derivative (1st order partial derivative) as a coefficient. On the contrary, in order to extract the 1st/2nd order partial derivatives from this potential by partial differential, it requires partial differentiation with these partial derivatives considered to be a constant. The reason that they can be realized is attributable to the zero result of the linear form which has as the coefficient a 3rd order partial derivative concerning the variable of integration in a primitive function. If this relation is used, the integral calculation and description may be simplified. An explanation was given with examples enumerated so that these conditions might be understood.}

place = {Japan}

year = {1996}

month = {May}

}

title = {Potential of a polygonal prism and lamina; Takakuchu men no potential}

author = {Koyama, S}

abstractNote = {With the use of rectangular coordinates O-XYZ, the potential of a calculation point P is expressed in the form of a triple repeated integral of a density {sigma} at point Q in the mass. The potential at the density {sigma} assumed to be 1 is named the potential of a polygonal prism. Further, a double repeated integral with an integral concerning Z removed from the triple integral is named the potential of polygonal lamina. This potential can be expressed in a quadratic form (linear form) with 2nd order partial derivative (1st order partial derivative) as a coefficient. On the contrary, in order to extract the 1st/2nd order partial derivatives from this potential by partial differential, it requires partial differentiation with these partial derivatives considered to be a constant. The reason that they can be realized is attributable to the zero result of the linear form which has as the coefficient a 3rd order partial derivative concerning the variable of integration in a primitive function. If this relation is used, the integral calculation and description may be simplified. An explanation was given with examples enumerated so that these conditions might be understood.}

place = {Japan}

year = {1996}

month = {May}

}