O'Reilly logo

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

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

8.57 Lommel functions

8.570 Definitions of the Lommel functions sμν(z) and Sμν(z):

1.12 

sμ,v(z)=m=0(1)mzμ+1+2m[(μ+1)2v2][(μ+3)2v2][(μ+2m+1)2v2]???????????????????????????????[μ±v?is?not?a?negative?odd?integer]=zμ1m=0(1)m(z2)2m+2Γ(12μ12v+12)Γ(12μ+12v+12)Γ(12μ12v+m+32)Γ(12μ+12v+m+32)???????????????????????????????????????????????????????[μ±v?is?not?a?negative?odd?integer]

si1107_e  EH II 40(69), WA 377(2)

2.12 

Sμ,v(z)=sμ,v(z)+2μ1Γ(12μ12v+12)Γ(12μ+12v+12)×cos[12(μv)π]Jv(z)cos[12(μ+v)π]Jv(z)sinvπ       [μ±v?is?a?positive?odd?integer,v?is?an?odd?integer]

  EH II 40(71), WA 379(2)

=sμ,v(z)+2μ1Γ(12μ12v+12)Γ(12μ+12v+12)×{sin[12(μ

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required