Application of maple on evaluating multiple improper integrals

Application of Parseval’s Theorem on Evaluating Some Definite Integrals

“…We can obtain the infinite series forms of these definite integrals by using Parseval's theorem; these are the major results of this paper (i.e., Theorems 1 and 2). As for the study of related integral problems can refer to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. On the other hand, we propose some definite integrals to do calculation practically.…”

Evaluating Multiple Integrals Using Maple

“…Moreover, we obtain some corollaries from these two theorems. For the study of related multiple integral problems can refer to [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In addition, we provide some multiple integrals to do calculation practically.…”

“…Using Maple to verify the correctness of(20) as follows: >evalf(Doubleint(exp(-5*x1-4*x2)*(cosh(7*x1+4*x2))^(2/ 3),x1=-4..-2,x2=-2..3),22); >evalf(1/2^(2/3)*sum(product(2/3-j,j=0..(m-1))/m! *(exp(58 /3-28*m)-exp(116/3-56*m))*(exp(-20+24*m)-exp(40/3-16 *m))/((-29/3+14*m)*(-20/3+8*m)),m=0..infinity),22); On the other hand, by Case (A) of Corollary 1, we obtain of (21) as follows: >evalf(Doubleint(exp(-5*x1-4*x2)*(cosh(7*x1+4*x2))^(2/ 3),x1=0..infinity,x2=0..infinity)); 1.420430140 >evalf(1/2^(2/3)*sum(product(2/3-j,j=0..(m-1))/(m!…”

Solving Some Definite Integrals by Using Maple

“…We can obtain the closed forms of these two types of definite integrals by using differentiation with respect to a parameter and Leibniz differential rule ; these are the main results of this paper (i.e., Theorems 1, 2). The study of related integral problems can refer to [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Simultaneously, we can compare the method used in this article with that in [27].…”