New Recursive Representations for the Favard Constants with Application to Multiple Singular Integrals and Summation of Series

Table 1

Exact and approximate values of the Favard constants 𝐾_𝑟, calculated by the recursive formulas (7a) and (7b) using Mathematica software package.

𝑟	Exact values of 𝐾𝑟	Approximate values of 𝐾𝑟
1	𝜋/2	1.5707963267948966192313216916
2	𝜋^2/8	1.2337005501361698273543113749
3	𝜋^3/24	1.2919281950124925073115131277
4	5𝜋^4/384	1.2683475395052400681828168318
5	𝜋^5/240	1.2750820199386727219280887918
6	61𝜋^6/46080	1.2726723265645306132561498711
7	17𝜋^7/40320	1.2734371248066831633864461900
8	277𝜋^8/2064384	1.2731754806526058136347769671
9	31𝜋^9/725760	1.2732612424724875463814366656
10	50521𝜋^10/3715891200	1.2732323827293948495082797108
11	691𝜋^11/159667200	1.2732419458721540967715077901
12	540553𝜋^12/392398110720	1.2732387471572495304117396905