About the Project
NIST

integrals of modified Bessel functions

AdvancedHelp

(0.014 seconds)

1—10 of 59 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: 10.1 Special Notation
For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).
3: 10.76 Approximations
§10.76(ii) Bessel Functions, Hankel Functions, and Modified Bessel Functions
4: 10.43 Integrals
§10.43(i) Indefinite Integrals
§10.43(iii) Fractional Integrals
§10.43(iv) Integrals over the Interval ( 0 , )
5: 6.10 Other Series Expansions
§6.10(ii) Expansions in Series of Spherical Bessel Functions
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 ) ) .
6: 10.74 Methods of Computation
§10.74(vii) Integrals
7: 10.44 Sums
§10.44(iv) Compendia
8: 10.75 Tables
§10.75(v) Modified Bessel Functions and their Derivatives
§10.75(vii) Integrals of Modified Bessel Functions
9: 8.6 Integral Representations
8.6.6 Γ ( a , z ) = 2 z 1 2 a e - z Γ ( 1 - a ) 0 e - t t - 1 2 a K a ( 2 z t ) d t , a < 1 ,
10: Bibliography T
  • N. M. Temme (1990b) Uniform asymptotic expansions of a class of integrals in terms of modified Bessel functions, with application to confluent hypergeometric functions. SIAM J. Math. Anal. 21 (1), pp. 241–261.
  • N. M. Temme (1994c) Steepest descent paths for integrals defining the modified Bessel functions of imaginary order. Methods Appl. Anal. 1 (1), pp. 14–24.
  • N. M. Temme (1978) The numerical computation of special functions by use of quadrature rules for saddle point integrals. II. Gamma functions, modified Bessel functions and parabolic cylinder functions. Report TW 183/78 Mathematisch Centrum, Amsterdam, Afdeling Toegepaste Wiskunde.