temp1 REVIEWED

This is the Title PhL 1.11.15 Want to show the first line here. 1/ = (1/π) Σn=0∞ εn Qn-1/2(a/b) cos(nx) // expansion !Syntax Error, Idx cos(nx)/ = Qn-1/2(a/b) // projection (10.3) Plan B. The second equation I claim is GR7 p961 8.713.1 with μ = 0 and ν = n-1/2). But I look at it and it says This looks like a bad reference. But wait : cos(νπ) = cos((n-1/2)π) = cos(nπ-π/2) = cos(π/2-nπ) = +sin(nπ) = 0 ν = n-1/2 so the second term goes away. The first term then gives Qn-1/2(z) = (1/2π)1/2 Γ(1/2) !Syntax Error, I cos(nt) dt/(z-cost)1/2 = (1/) !Syntax Error, Idx cos(nx) / Qn-1/2(a/b) = (1/)!Syntax Error, I dx cos(nx) / = !Syntax Error, I dx cos(nx) /[ ] Then !Syntax Error, I dx cos(nx) /[ ] = Qn-1/2(a/b) and yes, this does give my second equation above. Now what happens if we stick THIS thing into first equation above: (1/π) Σn=0∞ εn {Qn-1/2(a/b)} cos(nx) = (1/π) Σn=0∞ εn {!Syntax Error, I dy cos(ny) /[ ]} cos(nx) = (1/π) !Syntax Error, I dy (1/ ) Σn=0∞ εn cos(ny)cos(nx) = (1/π) !Syntax Error, I dy (1/ ) { π δ(x-y)} = 1/ and this agrees with the second equation at the start. Just now I went and repaired my Transform doc for an error with completeness statements. That error is documented in a new section there. So here is corrected info for the cosine transform. f(θ) = a0/2 + Σn=1∞ an cos(nθ) = (1/2) Σn=0∞ εn an cos(nθ) // expansion an = (2/π) !Syntax Error, Idθ f(θ) cos(nθ) where εn = 2-δn,0 // projection !Syntax Error, I dθ cos(nθ)cos(n'θ) = (π/εn) δnn' // orthogonality Σn=0∞εncos(nθ)cos(nθ)= π δ(θ-θ') // completeness It is this completeness that I use above! Probably this result also appears in IT for cosine transforms, but it is not there!!! So I will definitely be writing this up in an Appendix H section.