W. Lang, Apr 30 2010
A176730  and A176731

The two independent power series f(z) and g(z) related to Airy functions Ai(z) and Bi(z).

See the Abramowitz-Stegun handbook, 10.4 Airy Functions with plots.

f(z):=sum((1/A176730(n))*z^(3*n),n=0..infty)  is the series 

f(z) =1+(1/6)*z^3+(1/180)*z^6+(1/12960)*z^9+(1/1710720)*z^12+(1/359251200)*z^15+(1/109930867200)*z^18+(1/46170964224000)*z^21+(1/25486372251648000)*z^24+
   (1/17891433320656896000)*z^27+(1/15565546988971499520000)*z^30+(1/16437217620353903493120000)*z^33+(1/20710894201645918401331200000)*z^36+
   (1/30693545206839251070772838400000)*z^39+(1/52854284846177190343870827724800000)*z^42+(1/104651483995430836880864238895104000000)*z^45+
   (1/236093747893691968003229722947354624000000)*z^48+(1/602039057128914518408235793515754291200000000)*z^51+
   (1/1723035781502953351684370841042088781414400000000)*z^54+(1/5499930214557427098576511724606347390274764800000000)*z^57+
   (1/19469752959533291928960851505106469761572667392000000000)*z^60 + ...  

g(z):=sum((1/A176731(n))*z^(3*n+1),n=0..infty)  is the series 

g(z) = z+(1/12)*z^4+(1/504)*z^7+(1/45360)*z^10+(1/7076160)*z^13+(1/1698278400)*z^16+(1/580811212800)*z^19+(1/268334780313600)*z^22+(1/161000868188160000)*z^25+
   (1/121716656350248960000)*z^28+(1/113196490405731532800000)*z^31+(1/127006462235230779801600000)*z^34+(1/169172607697327398695731200000)*z^37+
   (1/263909268007830741965340672000000)*z^40+(1/476620138022142319989405253632000000)*z^43+(1/986603685705834602378068875018240000000)*z^46+
   (1/2320491868780122984793217994042900480000000)*z^49+(1/6153944436004886155671614120201772072960000000)*z^52+
   (1/18277214974934511882344693936999263056691200000000)*z^55+(1/60424472707133496283031558155719563665421107200000000)*z^58+
   (1/221153570108108596395895502849933603015441252352000000000)*z^61 +...

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