|
Kelvin Functions
In applied mathematics, the Kelvin functions ber''ν''(''x'') and bei''ν''(''x'') are the real and imaginary parts, respectively, of :J_\nu \left (x e^ \right ),\, where ''x'' is real, and , is the ''ν''th order Bessel function of the first kind. Similarly, the functions kerν(''x'') and keiν(''x'') are the real and imaginary parts, respectively, of :K_\nu \left (x e^ \right ),\, where is the ''ν''th order modified Bessel function of 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 With the exception of ber''n''(''x'') and bei''n''(''x'') for integral ''n'', the Kelvin functions have a branch point at ''x'' = 0. Below, is the gamma function and is the digamma function. ber(''x'') For integers ''n'', ber''n''(''x'') has the series expan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plot Of The Kelvin Function Ber(z) In The Complex Plane From -2-2i To 2+2i With Colors Created With Mathematica 13
Plot or Plotting may refer to: Art, media and entertainment * Plot (narrative), the story of a piece of fiction Music * ''The Plot'' (album), a 1976 album by jazz trumpeter Enrico Rava * The Plot (band), a band formed in 2003 Other * ''Plot'' (film), a 1973 French-Italian film * ''Plotting'' (video game), a 1989 Taito puzzle video game, also called Flipull * ''The Plot'' (video game), a platform game released in 1988 for the Amstrad CPC and Sinclair Spectrum * ''Plotting'' (non-fiction), a 1939 book on writing by Jack Woodford * ''The Plot'' (novel), a 2021 mystery by Jean Hanff Korelitz Graphics * Plot (graphics), a graphical technique for representing a data set * Plot (radar), a graphic display that shows all collated data from a ship's on-board sensors * Plot plan, a type of drawing which shows existing and proposed conditions for a given area Land * Plot (land), a piece of land used for building on ** Burial plot, a piece of land a person is buried in * Quadrat, a d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plot Of The Kelvin Function Bei(z) In The Complex Plane From -2-2i To 2+2i With Colors Created With Mathematica 13
Plot or Plotting may refer to: Art, media and entertainment * Plot (narrative), the story of a piece of fiction Music * ''The Plot'' (album), a 1976 album by jazz trumpeter Enrico Rava * The Plot (band), a band formed in 2003 Other * ''Plot'' (film), a 1973 French-Italian film * ''Plotting'' (video game), a 1989 Taito puzzle video game, also called Flipull * ''The Plot'' (video game), a platform game released in 1988 for the Amstrad CPC and Sinclair Spectrum * ''Plotting'' (non-fiction), a 1939 book on writing by Jack Woodford * ''The Plot'' (novel), a 2021 mystery by Jean Hanff Korelitz Graphics * Plot (graphics), a graphical technique for representing a data set * Plot (radar), a graphic display that shows all collated data from a ship's on-board sensors * Plot plan, a type of drawing which shows existing and proposed conditions for a given area Land * Plot (land), a piece of land used for building on ** Burial plot, a piece of land a person is buried in * Quadrat, a d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plot Of The Kelvin Function Kei(z) In The Complex Plane From -2-2i To 2+2i With Colors Created With Mathematica 13
Plot or Plotting may refer to: Art, media and entertainment * Plot (narrative), the story of a piece of fiction Music * ''The Plot'' (album), a 1976 album by jazz trumpeter Enrico Rava * The Plot (band), a band formed in 2003 Other * ''Plot'' (film), a 1973 French-Italian film * ''Plotting'' (video game), a 1989 Taito puzzle video game, also called Flipull * ''The Plot'' (video game), a platform game released in 1988 for the Amstrad CPC and Sinclair Spectrum * ''Plotting'' (non-fiction), a 1939 book on writing by Jack Woodford * ''The Plot'' (novel), a 2021 mystery by Jean Hanff Korelitz Graphics * Plot (graphics), a graphical technique for representing a data set * Plot (radar), a graphic display that shows all collated data from a ship's on-board sensors * Plot plan, a type of drawing which shows existing and proposed conditions for a given area Land * Plot (land), a piece of land used for building on ** Burial plot, a piece of land a person is buried in * Quadrat, a d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plot Of The Kelvin Function Ker(z) In The Complex Plane From -2-2i To 2+2i With Colors Created With Mathematica 13
Plot or Plotting may refer to: Art, media and entertainment * Plot (narrative), the story of a piece of fiction Music * ''The Plot'' (album), a 1976 album by jazz trumpeter Enrico Rava * The Plot (band), a band formed in 2003 Other * ''Plot'' (film), a 1973 French-Italian film * ''Plotting'' (video game), a 1989 Taito puzzle video game, also called Flipull * ''The Plot'' (video game), a platform game released in 1988 for the Amstrad CPC and Sinclair Spectrum * ''Plotting'' (non-fiction), a 1939 book on writing by Jack Woodford * ''The Plot'' (novel), a 2021 mystery by Jean Hanff Korelitz Graphics * Plot (graphics), a graphical technique for representing a data set * Plot (radar), a graphic display that shows all collated data from a ship's on-board sensors * Plot plan, a type of drawing which shows existing and proposed conditions for a given area Land * Plot (land), a piece of land used for building on ** Burial plot, a piece of land a person is buried in * Quadrat, a d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymptotic Series
In mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular, often infinite, point. Investigations by revealed that the divergent part of an asymptotic expansion is latently meaningful, i.e. contains information about the exact value of the expanded function. The most common type of asymptotic expansion is a power series in either positive or negative powers. Methods of generating such expansions include the Euler–Maclaurin summation formula and integral transforms such as the Laplace and Mellin transforms. Repeated integration by parts will often lead to an asymptotic expansion. Since a '' convergent'' Taylor series fits the definition of asymptotic expansion as well, the phrase "asymptotic series" usually implies a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Part
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a + bi, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number a+bi, is called the , and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with rea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
