UltrasphericalZeros

Zeros of Ultraspherical polynomials.

Interface

܀ Interface

INTERFACE
  MODULE FUNCTION UltrasphericalZeros(n, lambda) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: n
    !! order of Ultraspherical polynomial
    REAL(DFP), INTENT(IN) :: lambda
    !! lambda should be greater than -0.5
    REAL(DFP) :: ans(n)
  END FUNCTION UltrasphericalZeros
END INTERFACE

️܀ See example

This example shows the usage of UltrasphericalZeros method.

This routine returns the zeros of a jacobi polynomial.

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real( dfp ), allocatable :: pt( : )
  real( dfp ), parameter :: lambda=0.5_DFP
  type(string) :: msg, astr

  n = 1; call callme

See results

x
0

  n = 2; call callme

See results

Zeros of T(x), n = 2

-0.57735	0.57735

  n = 3; call callme

See results

Zeros of T(x), n = 3

-0.7746	3.71231E-16	0.7746

  contains
  subroutine callme
    pt = UltrasphericalZeros( n=n, lambda=lambda )
    msg = "Zeros of T(x), n = " &
        & // tostring( n )
    call display(msg%chars())
    astr = MdEncode( pt )
    call display( astr%chars(), "" )
  end subroutine

end program main

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