Several Integrability Formulas of Some Functions, Orthogonal Polynomials and Norm Functions

• Autorzy: Bo Li , Yanping Zhuang , Bing Xie , Pan Wang
• Języki publikacji: EN

Abstrakty

EN

In this article, we give several integrability formulas of some functions including the trigonometric function and the index function [3]. We also give the definitions of the orthogonal polynomial and norm function, and some of their important properties [19].MML identifier: INTEGRA9, version: 7.11.01 4.117.1046

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2009
• Tom: 17
• Numer: 1
• Strony: 11-21

Daty

wydano

2009-01-01

online

2009-03-20

Twórcy

autor

Bo Li

• Qingdao University of Science and Technology, China

autor

Yanping Zhuang

• Qingdao University of Science and Technology, China

autor

Bing Xie

• Qingdao University of Science and Technology, China

autor

Pan Wang

• Qingdao University of Science and Technology, China

Bibliografia

• [1] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
• [2] Czesław Byliński and Piotr Rudnicki. Bounding boxes for compact sets in ε2. Formalized Mathematics, 6(3):427-440, 1997.
• [3] Chuanzhang Chen. Mathematical Analysis. Higher Education Press, Beijing, 1978.
• [4] Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93-102, 1999.
• [5] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. Formalized Mathematics, 9(2):281-284, 2001.
• [6] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
• [7] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.
• [8] Jarosław Kotowicz. Partial functions from a domain to a domain. Formalized Mathematics, 1(4):697-702, 1990.
• [9] Jarosław Kotowicz. Partial functions from a domain to the set of real numbers. Formalized Mathematics, 1(4):703-709, 1990.
• [10] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
• [11] Konrad Raczkowski. Integer and rational exponents. Formalized Mathematics, 2(1):125-130, 1991.
• [12] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.
• [13] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
• [14] Yasunari Shidama. The Taylor expansions. Formalized Mathematics, 12(2):195-200, 2004.
• [15] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.
• [16] Andrzej Trybulec and Yatsuka Nakamura. On the decomposition of a simple closed curve into two arcs. Formalized Mathematics, 10(3):163-167, 2002.
• [17] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
• [18] Peng Wang and Bo Li. Several differentiation formulas of special functions. Part V. Formalized Mathematics, 15(3):73-79, 2007, doi:10.2478/v10037-007-0009-4.[Crossref]
• [19] Renhong Wang. Numerical approximation. Higher Education Press, Beijing, 1999.
• [20] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
• [21] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998.

Identyfikatory

DOI

10.2478/v10037-009-0002-1