458 D. BIERENS DE HAAN. NOUVELLES FORMULES DE REDUCTION. 



n ^ n ^ i 



— — - Sinpq.Z kn Cas nqs— - 2' knSin [ {ns~p)q \ =-L- p ^ as, 



^-.-Sinpq.\f,^{(l)—A,\—-2:AnS{n \{ns-p)q 



'\ 



[p ^ un, -| 

 '■ri 



(Vd) 



A ( 



J 



x) Sin px — — — - = — ^ Bo Cos pq— 



q^ — x^ ^ 



71 ^ n 



— — Cos pq . Z Bw Cos nqs:=z — - Cos pq ./^ (q'>, 



\p > as\ , . (Nid) 



:=: — - Bo Cos pq— - B« Cos 2pq — — Cospq .2. B« Cos nqs= ... ( VI6) 

 2 4 2 i 



= — - Eo Cos pq-h - B« — - Cos pq,Z B« Cos nqs = [/? = as\ , 

 Z 4 2 X l 



;.A('^)4-7B«, 



. . . (Vie) 



= — - B^Cospq — - Cos pq.I^^nCos nqs~\- - Sinpq.Z^BnSinnqs, 



(VI^) 



= — -BoCospq— ~ Cospq.ZBnCosnqs+ - i:BnCos\{ns-~p)q\—[ 

 ^ ^ 1 ^ d+\ 



n 71 " , 



= •— - (7o6^ pq.f^ [q) -i-- SBnCosI (ns—p) q , 



= — -Bq Cospq-\- - Sinpq.2^BnSinnqs— -i:BnCos \ {ns—p)q ) =| 



p-> as, 



s 

 fraction 



(Vie) 



— -Bo Cospq-^ ~ Sinpq. f^ (q)-~ ^ ^B« Cos \ {ns—p) q j , 



(VI/) 



d—\ 



= — - Bo Cos pq — - Cospq.Z B« Cos nqs — -Bu Cos2pq -i- 

 2i Z i 4 



+ - Sm pq. 2:Bn Sin nqs , 

 ^ d+l 



= — - B^^Cospq+ - B^—- Cospq.i:BnCosnqs+ - ^B« Co^j (;ns—p)q\ — 



^ 4 2 1 2^4.1 



=-- Cospq._f\_ (,y)4_^B^ + ^ 2^ B« (7o6- j [ns—p..q \ , 



^ 4 2^4.[ 



=— - BqCos pq— ~ Bd+ - Sinpq.ZBnSinnqs— - ZBnCos\{^ns~p)q\ — 



p-> as, 

 entier 



(VI?) 



(vi/0 



7T ^^ 71 



d—l 



=^— -BqCos pq—~Bd+ - Sinpq. f\ {q) — ^ ^ ^» ^^^ î i*^^—P)9 I • 



(VI/) 



