SciPy 0.6.0 API Documentation Generated by Endo, 2007-10-17
SciPy 0.6.0 API Documentation Generated by Endo, 2007-10-17
digamma = psi
sph_harm = vectorize(_sph_harmonic, 'D')
Arithmetic, Geometric Mean
Start with a_0=a and b_0=b and iteratively compute
a_{n+1} = (a_n+b_n)/2 b_{n+1} = sqrt(a_n*b_n)
until a_n=b_n. The result is agm(a,b)
agm(a,b)=agm(b,a) agm(a,a) = a min(a,b) < agm(a,b) < max(a,b)
Compute the zeros of Airy Functions Ai(x) and Ai'(x), a and a' respectively, and the associated values of Ai(a') and Ai'(a).
Outputs:
a[l-1] -- the lth zero of Ai(x) ap[l-1] -- the lth zero of Ai'(x) ai[l-1] -- Ai(ap[l-1]) aip[l-1] -- Ai'(a[l-1])
Compute nt zeros of the kelvin function bei x
Compute nt zeros of the kelvin function bei' x
Compute nt zeros of the kelvin function ber x
Return an array of the Bernoulli numbers B0..Bn
Compute nt zeros of the kelvin function ber' x
Compute the zeros of Airy Functions Bi(x) and Bi'(x), b and b' respectively, and the associated values of Ai(b') and Ai'(b).
Outputs:
b[l-1] -- the lth zero of Bi(x) bp[l-1] -- the lth zero of Bi'(x) bi[l-1] -- Bi(bp[l-1]) bip[l-1] -- Bi'(b[l-1])
Returns the periodic sinc function also called the dirichlet function: diric(x) = sin(x *n / 2) / (n sin(x / 2)) where n is a positive integer.
Compute nt complex zeros of the error function erf(z).
Return an array of the Euler numbers E0..En (inclusive)
Compute nt complex zeros of the sine and cosine fresnel integrals S(z) and C(z).
Compute nt complex zeros of the cosine fresnel integral C(z).
Compute nt complex zeros of the sine fresnel integral S(z).
returns the inverse of the incomplete gamma integral in that it finds x such that gammainc(a,x)=y
Return the nth derivative of H1v(z) with respect to z.
Return the nth derivative of H2v(z) with respect to z.
Confluent hypergeometric limit function 0F1. Limit as q->infinity of 1F1(q;a;z/q)
Return the nth derivative of Iv(z) with respect to z.
Compute nt zeros of the Bessel function Jn(x).
Compute nt (<=1400) zeros of the bessel functions Jn and Jn'
and arange them in order of their magnitudes.
Outputs (all are arrays of length nt):
zo[l-1] -- Value of the lth zero of of Jn(x) and Jn'(x)
n[l-1] -- Order of the Jn(x) or Jn'(x) associated with lth zero
m[l-1] -- Serial number of the zeros of Jn(x) or Jn'(x) associated
with lth zero.
t[l-1] -- 0 if lth zero in zo is zero of Jn(x), 1 if it is a zero
of Jn'(x)
See jn_zeros, jnp_zeros to get separated arrays of zeros.
Compute nt zeros of the Bessel function Jn'(x).
Compute nt zeros of the Bessel functions Jn(x), Jn'(x), Yn(x), and Yn'(x), respectively. Returns 4 arrays of length nt.
See jn_zeros, jnp_zeros, yn_zeros, ynp_zeros to get separate arrays.
Return the nth derivative of Jv(z) with respect to z.
Compute nt zeros of the kelvin function kei x
Compute nt zeros of the kelvin function kei' x
Compute nt zeros of all the kelvin functions returned in a length 8 tuple of arrays of length nt. The tuple containse the arrays of zeros of (ber, bei, ker, kei, ber', bei', ker', kei')
Compute nt zeros of the kelvin function ker x
Compute nt zeros of the kelvin function ker' x
Return the nth derivative of Kv(z) with respect to z.
Compute sequence of lambda functions with arbitrary order v and their derivatives. Lv0(x)..Lv(x) are computed with v0=v-int(v).
Associated Legendre functions of the first kind, Pmn(z) and its derivative, Pmn'(z) of order m and degree n. Returns two arrays of size (m+1,n+1) containing Pmn(z) and Pmn'(z) for all orders from 0..m and degrees from 0..n.
z can be complex.
Compute sequence of Legendre functions of the first kind (polynomials), Pn(z) and derivatives for all degrees from 0 to n (inclusive).
See also special.legendre for polynomial class.
Associated Legendre functions of the second kind, Qmn(z) and its derivative, Qmn'(z) of order m and degree n. Returns two arrays of size (m+1,n+1) containing Qmn(z) and Qmn'(z) for all orders from 0..m and degrees from 0..n.
z can be complex.
Compute sequence of Legendre functions of the second kind, Qn(z) and derivatives for all degrees from 0 to n (inclusive).
Compute expansion coefficients for even mathieu functions and modified mathieu functions.
Compute expansion coefficients for even mathieu functions and modified mathieu functions.
Compute a sequence of characteristic values for the oblate spheroidal wave functions for mode m and n'=m..n and spheroidal parameter c.
Compute sequence of parabolic cylinder functions Dn(z) and their derivatives for D0(z)..Dn(z).
Compute sequence of parabolic cylinder functions Dv(x) and their derivatives for Dv0(x)..Dv(x) with v0=v-int(v).
Compute sequence of parabolic cylinder functions Dv(x) and their derivatives for Dv0(x)..Dv(x) with v0=v-int(v).
Polygamma function which is the nth derivative of the digamma (psi) function.
Compute a sequence of characteristic values for the prolate spheroidal wave functions for mode m and n'=m..n and spheroidal parameter c.
Compute the Ricatti-Bessel function of the first kind and its derivative for all orders up to and including n.
Compute the Ricatti-Bessel function of the second kind and its derivative for all orders up to and including n.
Returns sin(pi*x)/(pi*x) at all points of array x.
Compute the spherical Bessel function in(z) and its derivative for all orders up to and including n.
Compute the spherical Bessel functions, in(z) and kn(z) and their derivatives for all orders up to and including n.
Compute the spherical Bessel function jn(z) and its derivative for all orders up to and including n.
Compute the spherical Bessel functions, jn(z) and yn(z) and their derivatives for all orders up to and including n.
Compute the spherical Bessel function kn(z) and its derivative for all orders up to and including n.
Compute the spherical Bessel function yn(z) and its derivative for all orders up to and including n.
Returns nt (complex or real) zeros of Y0(z), z0, and the value of Y0'(z0) = -Y1(z0) at each zero.
Returns nt (complex or real) zeros of Y1(z), z1, and the value of Y1'(z1) = Y0(z1) at each zero.
Returns nt (complex or real) zeros of Y1'(z), z1', and the value of Y1(z1') at each zero.
Compute nt zeros of the Bessel function Yn(x).
Compute nt zeros of the Bessel function Yn'(x).
Return the nth derivative of Yv(z) with respect to z.
| Local name | Refers to |
|---|---|
| specfun | SciPy.special.specfun |
| types | types |
| __bootstrap__ | SciPy.special._cephes.__bootstrap__ |