About the Project

Bessel integral

AdvancedHelp

(0.006 seconds)

1—10 of 95 matching pages

1: 10.32 Integral Representations
§10.32(i) Integrals along the Real Line
Basset’s Integral
§10.32(ii) Contour Integrals
§10.32(iii) Products
§10.32(iv) Compendia
2: 10.43 Integrals
§10.43(i) Indefinite Integrals
§10.43(iii) Fractional Integrals
§10.43(iv) Integrals over the Interval ( 0 , )
3: 10.59 Integrals
§10.59 Integrals
10.59.1 e i b t 𝗃 n ( t ) d t = { π i n P n ( b ) , 1 < b < 1 , 1 2 π ( ± i ) n , b = ± 1 , 0 , ± b > 1 ,
For an integral representation of the Dirac delta in terms of a product of spherical Bessel functions of the first kind see §1.17(ii), and for a generalization see Maximon (1991). …
4: 10.1 Special Notation
For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).
5: 10.9 Integral Representations
Bessel’s Integral
Neumann’s Integral
Poisson’s and Related Integrals
§10.9(ii) Contour Integrals
Schläfli’s Integral
6: 6.10 Other Series Expansions
§6.10(ii) Expansions in Series of Spherical Bessel Functions
6.10.4 Si ( z ) = z n = 0 ( 𝗃 n ( 1 2 z ) ) 2 ,
6.10.5 Cin ( z ) = n = 1 a n ( 𝗃 n ( 1 2 z ) ) 2 ,
6.10.6 Ei ( x ) = γ + ln | x | + n = 0 ( 1 ) n ( x a n ) ( 𝗂 n ( 1 ) ( 1 2 x ) ) 2 , x 0 ,
6.10.8 Ein ( z ) = z e z / 2 ( 𝗂 0 ( 1 ) ( 1 2 z ) + n = 1 2 n + 1 n ( n + 1 ) 𝗂 n ( 1 ) ( 1 2 z ) ) .
7: 10.76 Approximations
§10.76(ii) Bessel Functions, Hankel Functions, and Modified Bessel Functions
8: 10.74 Methods of Computation
For evaluation of the Hankel functions H ν ( 1 ) ( z ) and H ν ( 2 ) ( z ) for complex values of ν and z based on the integral representations (10.9.18) see Remenets (1973). …
§10.74(vii) Integrals
Spherical Bessel Transform
For infinite integrals involving products of Bessel functions of the first kind, see Linz and Kropp (1973), Gabutti (1980), Ikonomou et al. (1995), Lucas (1995), and Van Deun and Cools (2008). For infinite integrals involving products of Bessel functions of the first and second kinds, see Ratnanather et al. (2014). …
9: 10.22 Integrals
Products
Trigonometric Arguments
Convolutions
Fractional Integral
Weber–Schafheitlin Discontinuous Integrals, including Special Cases
10: 10.38 Derivatives with Respect to Order