In applied mathematics, the Kelvin functions ber ν ( x ) and bei ν ( x ) are the real and imaginary parts , respectively, of
10-558: [REDACTED] Look up bei or 北 in Wiktionary, the free dictionary. Bei may refer to: North , commonly encountered as 北 ( Mandarin : běi ) in Chinese placenames Chinese stelae ( 碑 , bēi ) Bei River , a tributary of the Pearl River in southern China Bei (surname) (贝/貝), a Chinese surname ( mathematics ) bei,
20-402: A Kelvin function Yelü Bei (899–937), Khitan prince (Yelü being his clan name) See also [ edit ] [REDACTED] Search for "bei" , "b-ei" , "be-i" , "b-e-i" , or "beis" on Misplaced Pages. BEI (disambiguation) All pages with titles beginning with Bei All pages with titles containing bei Bey Topics referred to by
30-485: A branch point at x = 0. Below, Γ( z ) is the gamma function and ψ ( z ) is the digamma function . For integers n , ber n ( x ) has the series expansion where Γ( z ) is the gamma function . The special case ber 0 ( x ), commonly denoted as just ber( x ), has the series expansion and asymptotic series where For integers n , bei n ( x ) has the series expansion The special case bei 0 ( x ), commonly denoted as just bei( x ), has
40-413: Is different from Wikidata All article disambiguation pages All disambiguation pages bei [REDACTED] Look up bei or 北 in Wiktionary, the free dictionary. Bei may refer to: North , commonly encountered as 北 ( Mandarin : běi ) in Chinese placenames Chinese stelae ( 碑 , bēi ) Bei River , a tributary of
50-399: Is different from Wikidata All article disambiguation pages All disambiguation pages Kelvin function where x is real, and J ν ( z ) , is the ν order Bessel function of the first kind. Similarly, the functions ker ν ( x ) and kei ν ( x ) are the real and imaginary parts, respectively, of where K ν ( z ) is the ν order modified Bessel function of
60-504: The Pearl River in southern China Bei (surname) (贝/貝), a Chinese surname ( mathematics ) bei, a Kelvin function Yelü Bei (899–937), Khitan prince (Yelü being his clan name) See also [ edit ] [REDACTED] Search for "bei" , "b-ei" , "be-i" , "b-e-i" , or "beis" on Misplaced Pages. BEI (disambiguation) All pages with titles beginning with Bei All pages with titles containing bei Bey Topics referred to by
70-450: The same term [REDACTED] This disambiguation page lists articles associated with the title Bei . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Bei&oldid=1175060299 " Category : Disambiguation pages Hidden categories: Articles containing Chinese-language text Short description
80-450: The same term [REDACTED] This disambiguation page lists articles associated with the title Bei . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Bei&oldid=1175060299 " Category : Disambiguation pages Hidden categories: Articles containing Chinese-language text Short description
90-452: The second kind. These functions are named after William Thomson, 1st Baron Kelvin . While the Kelvin functions are defined as the real and imaginary parts of Bessel functions with x taken to be real, the functions can be analytically continued for complex arguments xe , 0 ≤ φ < 2 π . With the exception of ber n ( x ) and bei n ( x ) for integral n , the Kelvin functions have
100-399: The series expansion and asymptotic series where α, f 1 ( x ) {\displaystyle f_{1}(x)} , and g 1 ( x ) {\displaystyle g_{1}(x)} are defined as for ber( x ). For integers n , ker n ( x ) has the (complicated) series expansion The special case ker 0 ( x ), commonly denoted as just ker( x ), has
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