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This book focuses on the ellipsoidal function, which serves as an evolution and extension of the circular function (trigonometric function) and elliptic function. It presents an in-depth discussion of the ellipsoidal function (algebra) theory and the conformal mapping (geometry) theory of the ellipsoid function, demonstrating the outstanding performance of the ellipsoid function response filter. Applications of the ellipsoidal function include the capacitance of ellipsoidal conductors and the surface area of ellipsoids, which in turn correspond to ellipsoidal integrals of the first kind and the second kind, respectively. The book offers a valuable reference guide for undergraduates, graduate students and researchers in the related fields. 

Notes on the Ellipsoidal Function

From Circular Integral to Ellipsoidal Integral.- Application Background of Circular Integral.- Application Background of Elliptic Integral.- Application Background of Ellipsoidal Integral.- Ellipsoidal Function Theory.- Conformal Mapping of Ellipsoidal Function.- Network of Ellipsoidal Function.- Application of Ellipsoidal Function.