# §28.28 Integrals, Integral Representations, and Integral Equations

## §28.28(i) Equations with Elementary Kernels

Let

Then

In (28.28.7)–(28.28.9) the paths of integration are given by

28.28.6

where and are real constants.

where the upper or lower sign is taken according as or . For and see §§28.4 and 28.5(i).

For details and further equations see Meixner et al. (1980, §2.1.1) and Sips (1970).

## §28.28(ii) Integrals of Products with Bessel Functions

In particular, for integer and ,

where again and , .

## §28.28(iii) Integrals of Products of Mathieu Functions of Noninteger Order

With the parameter suppressed we use the notation

28.28.24

and assume and . Then

28.28.25
28.28.26

where

## §28.28(iv) Integrals of Products of Mathieu Functions of Integer Order

Let

28.28.39
28.28.40

Then

28.28.41
28.28.42

where , ; , . Also,

## §28.28(v) Compendia

See Prudnikov et al. (1990, pp. 359–368), Gradshteyn and Ryzhik (2000, pp. 755–759), Sips (1970), and Meixner et al. (1980, §2.1.1).