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**11 - 18**of**18**### Several Integrability Formulas of Some Functions, Orthogonal Polynomials and Norm Functions

"... Summary. 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]. ..."

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Summary. 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].

### Several Differentiation Formulas of Special Functions. Part VII

"... Summary. In this article, we prove a series of differentiation identities [2] involving the arctan and arccot functions and specific combinations of special functions including trigonometric and exponential functions. ..."

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Summary. In this article, we prove a series of differentiation identities [2] involving the arctan and arccot functions and specific combinations of special functions including trigonometric and exponential functions.

### Riemann Indefinite Integral of Functions of Real Variable

, 2007

"... In this article we define the Riemann indefinite integral of functions of real variable and prove the linearity of that [1]. And we give some examples of the indefinite integral of some elementary functions. Furthermore, also the theorem about integral operation and uniform convergent sequence of fu ..."

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In this article we define the Riemann indefinite integral of functions of real variable and prove the linearity of that [1]. And we give some examples of the indefinite integral of some elementary functions. Furthermore, also the theorem about integral operation and uniform convergent sequence of functions is proved.

### Several Higher Differentiation Formulas of Special Functions

"... Summary. In this paper, we proved some basic properties of higher dif-ferentiation, and higher differentiation formulas of special functions [4]. ..."

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Summary. In this paper, we proved some basic properties of higher dif-ferentiation, and higher differentiation formulas of special functions [4].

### Integrability Formulas. Part I

, 2010

"... In this article, we give several differentiation and integrability formulas of special and composite functions including the trigonometric function, and the polynomial function. ..."

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In this article, we give several differentiation and integrability formulas of special and composite functions including the trigonometric function, and the polynomial function.

### Difference and Difference Quotient. Part IV

, 2011

"... Summary. In this article, we give some important theorems of forward difference, backward difference, central difference and difference quotient and forward difference, backward difference, central difference and difference quotient formulas of some special functions. ..."

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Summary. In this article, we give some important theorems of forward difference, backward difference, central difference and difference quotient and forward difference, backward difference, central difference and difference quotient formulas of some special functions.

### Definiton and some properties . . .

, 2007

"... In this article we mainly define the information entropy [3], [11] and prove some its basic properties. First, we discuss some properties on four kinds of transformation functions between vector and matrix. The transformation functions are LineVec2Mx, ColVec2Mx, Vec2DiagMx and Mx2FinS. Mx2FinS is ..."

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In this article we mainly define the information entropy [3], [11] and prove some its basic properties. First, we discuss some properties on four kinds of transformation functions between vector and matrix. The transformation functions are LineVec2Mx, ColVec2Mx, Vec2DiagMx and Mx2FinS. Mx2FinS is a horizontal concatenation operator for a given matrix, treating rows of the given matrix as finite sequences, yielding a new finite sequence by horizontally joining each row of the given matrix in order to index. Then we define each concept of information entropy for a probability sequence and two kinds of probability matrices, joint and conditional, that are defined in article [25]. Further, we discuss some properties of information entropy including Shannonâ€™s lemma, maximum property, additivity and super-additivity properties.

### Several Dierentiation Formulas of Special Functions. Part VI

"... Summary. In this article, we prove a series of dierentiation identities [3] involving the secant and cosecant functions and specic combinations of special functions including trigonometric, exponential and logarithmic functions. MML identier: FDIFF 10, version: 7.8.05 4.89.993 ..."

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Summary. In this article, we prove a series of dierentiation identities [3] involving the secant and cosecant functions and specic combinations of special functions including trigonometric, exponential and logarithmic functions. MML identier: FDIFF 10, version: 7.8.05 4.89.993