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Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

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6.8 Functions Generated by Bessel Functions

6.81 Struve functions

6.811

1. 

0Hν(bx)dx=cot(νπ2)b[2<Reν<0,????b>0]

si1818_e  ET II 158(1)

2. 

0Hν(a2x)?Hν(bx)dx=J2ν(2ab)b[a>0,????b>0,???Reν>32]

si1819_e  ET II 170(37)

3. 

0Hν1(a2x)?Hν(bx)dxx=1abJ2ν1(2ab)[a>0,???b>0,?????Reν>12]

si1820_e  ET II 170(38)

6.812

1. 

0H1(bx)dxx2+a2=π2a[I1(ab)L1(ab)][Rea>0,????b>0]

  ET II 158(6)

2. 

0Hν(bx)x2+a2dx=π2asin(νπ2)Lν(ab)+bcot(νπ2)1ν2F12(1;3ν2;3+ν2;a2b22)

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