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# Cython API for special functions

Scalar, typed versions of many of the functions in `scipy.special` can be accessed directly from Cython; the complete list is given below. Functions are overloaded using Cython fused types so their names match their Python counterpart. The module follows the following conventions:

- If a function’s Python counterpart returns multiple values, then the function returns its outputs via pointers in the final arguments.

- If a function’s Python counterpart returns a single value, then the function’s output is returned directly.

The module is usable from Cython via:

    cimport scipy.special.cython_special

## Error handling

Functions can indicate an error by returning `nan`; however they cannot emit warnings like their counterparts in `scipy.special`.

## Available functions

- `voigt_profile`:

      double voigt_profile(double, double, double)

- `agm`:

      double agm(double, double)

- `airy`:

      void airy(double, double *, double *, double *, double *)
      void airy(double complex, double complex *, double complex *, double complex *, double complex *)

- `airye`:

      void airye(double complex, double complex *, double complex *, double complex *, double complex *)
      void airye(double, double *, double *, double *, double *)

- `bdtr`:

      double bdtr(double, double, double)
      double bdtr(double, long, double)

- `bdtrc`:

      double bdtrc(double, double, double)
      double bdtrc(double, long, double)

- `bdtri`:

      double bdtri(double, double, double)
      double bdtri(double, long, double)

- `bdtrik`:

      double bdtrik(double, double, double)

- `bdtrin`:

      double bdtrin(double, double, double)

- `bei`:

      double bei(double)

- `beip`:

      double beip(double)

- `ber`:

      double ber(double)

- `berp`:

      double berp(double)

- `besselpoly`:

      double besselpoly(double, double, double)

- `beta`:

      double beta(double, double)

- `betainc`:

      float betainc(float, float, float)
      double betainc(double, double, double)

- `betaincc`:

      float betaincc(float, float, float)
      double betaincc(double, double, double)

- `betaincinv`:

      float betaincinv(float, float, float)
      double betaincinv(double, double, double)

- `betainccinv`:

      float betainccinv(float, float, float)
      double betainccinv(double, double, double)

- `betaln`:

      double betaln(double, double)

- `binom`:

      double binom(double, double)

- `boxcox`:

      double boxcox(double, double)

- `boxcox1p`:

      double boxcox1p(double, double)

- `btdtria`:

      double btdtria(double, double, double)

- `btdtrib`:

      double btdtrib(double, double, double)

- `cbrt`:

      double cbrt(double)

- `chdtr`:

      double chdtr(double, double)

- `chdtrc`:

      double chdtrc(double, double)

- `chdtri`:

      double chdtri(double, double)

- `chdtriv`:

      double chdtriv(double, double)

- `chndtr`:

      double chndtr(double, double, double)

- `chndtridf`:

      double chndtridf(double, double, double)

- `chndtrinc`:

      double chndtrinc(double, double, double)

- `chndtrix`:

      double chndtrix(double, double, double)

- `cosdg`:

      double cosdg(double)

- `cosm1`:

      double cosm1(double)

- `cotdg`:

      double cotdg(double)

- `dawsn`:

      double dawsn(double)
      double complex dawsn(double complex)

- `ellipe`:

      double ellipe(double)

- `ellipeinc`:

      double ellipeinc(double, double)

- `ellipj`:

      void ellipj(double, double, double *, double *, double *, double *)

- `ellipkinc`:

      double ellipkinc(double, double)

- `ellipkm1`:

      double ellipkm1(double)

- `ellipk`:

      double ellipk(double)

- `elliprc`:

      double elliprc(double, double)
      double complex elliprc(double complex, double complex)

- `elliprd`:

      double elliprd(double, double, double)
      double complex elliprd(double complex, double complex, double complex)

- `elliprf`:

      double elliprf(double, double, double)
      double complex elliprf(double complex, double complex, double complex)

- `elliprg`:

      double elliprg(double, double, double)
      double complex elliprg(double complex, double complex, double complex)

- `elliprj`:

      double elliprj(double, double, double, double)
      double complex elliprj(double complex, double complex, double complex, double complex)

- `entr`:

      double entr(double)

- `erf`:

      double complex erf(double complex)
      double erf(double)

- `erfc`:

      double complex erfc(double complex)
      double erfc(double)

- `erfcx`:

      double erfcx(double)
      double complex erfcx(double complex)

- `erfi`:

      double erfi(double)
      double complex erfi(double complex)

- `erfinv`:

      float erfinv(float)
      double erfinv(double)

- `erfcinv`:

      double erfcinv(double)

- `eval_chebyc`:

      double complex eval_chebyc(double, double complex)
      double eval_chebyc(double, double)
      double eval_chebyc(Py_ssize_t, double)

- `eval_chebys`:

      double complex eval_chebys(double, double complex)
      double eval_chebys(double, double)
      double eval_chebys(Py_ssize_t, double)

- `eval_chebyt`:

      double complex eval_chebyt(double, double complex)
      double eval_chebyt(double, double)
      double eval_chebyt(Py_ssize_t, double)

- `eval_chebyu`:

      double complex eval_chebyu(double, double complex)
      double eval_chebyu(double, double)
      double eval_chebyu(Py_ssize_t, double)

- `eval_gegenbauer`:

      double complex eval_gegenbauer(double, double, double complex)
      double eval_gegenbauer(double, double, double)
      double eval_gegenbauer(Py_ssize_t, double, double)

- `eval_genlaguerre`:

      double complex eval_genlaguerre(double, double, double complex)
      double eval_genlaguerre(double, double, double)
      double eval_genlaguerre(Py_ssize_t, double, double)

- `eval_hermite`:

      double eval_hermite(Py_ssize_t, double)

- `eval_hermitenorm`:

      double eval_hermitenorm(Py_ssize_t, double)

- `eval_jacobi`:

      double complex eval_jacobi(double, double, double, double complex)
      double eval_jacobi(double, double, double, double)
      double eval_jacobi(Py_ssize_t, double, double, double)

- `eval_laguerre`:

      double complex eval_laguerre(double, double complex)
      double eval_laguerre(double, double)
      double eval_laguerre(Py_ssize_t, double)

- `eval_legendre`:

      double complex eval_legendre(double, double complex)
      double eval_legendre(double, double)
      double eval_legendre(Py_ssize_t, double)

- `eval_sh_chebyt`:

      double complex eval_sh_chebyt(double, double complex)
      double eval_sh_chebyt(double, double)
      double eval_sh_chebyt(Py_ssize_t, double)

- `eval_sh_chebyu`:

      double complex eval_sh_chebyu(double, double complex)
      double eval_sh_chebyu(double, double)
      double eval_sh_chebyu(Py_ssize_t, double)

- `eval_sh_jacobi`:

      double complex eval_sh_jacobi(double, double, double, double complex)
      double eval_sh_jacobi(double, double, double, double)
      double eval_sh_jacobi(Py_ssize_t, double, double, double)

- `eval_sh_legendre`:

      double complex eval_sh_legendre(double, double complex)
      double eval_sh_legendre(double, double)
      double eval_sh_legendre(Py_size_t, double)

- `exp1`:

      double complex exp1(double complex)
      double exp1(double)

- `exp10`:

      double exp10(double)

- `exp2`:

      double exp2(double)

- `expi`:

      double complex expi(double complex)
      double expi(double)

- `expit`:

      double expit(double)
      float expit(float)
      long double expit(long double)

- `expm1`:

      double complex expm1(double complex)
      double expm1(double)

- `expn`:

      double expn(double, double)
      double expn(long, double)

- `exprel`:

      double exprel(double)

- `fdtr`:

      double fdtr(double, double, double)

- `fdtrc`:

      double fdtrc(double, double, double)

- `fdtri`:

      double fdtri(double, double, double)

- `fdtridfd`:

      double fdtridfd(double, double, double)

- `fresnel`:

      void fresnel(double, double *, double *)
      void fresnel(double complex, double complex *, double complex *)

- `gamma`:

      double complex gamma(double complex)
      double gamma(double)

- `gammainc`:

      double gammainc(double, double)

- `gammaincc`:

      double gammaincc(double, double)

- `gammainccinv`:

      double gammainccinv(double, double)

- `gammaincinv`:

      double gammaincinv(double, double)

- `gammaln`:

      double gammaln(double)

- `gammasgn`:

      double gammasgn(double)

- `gdtr`:

      double gdtr(double, double, double)

- `gdtrc`:

      double gdtrc(double, double, double)

- `gdtria`:

      double gdtria(double, double, double)

- `gdtrib`:

      double gdtrib(double, double, double)

- `gdtrix`:

      double gdtrix(double, double, double)

- `hankel1`:

      double complex hankel1(double, double complex)

- `hankel1e`:

      double complex hankel1e(double, double complex)

- `hankel2`:

      double complex hankel2(double, double complex)

- `hankel2e`:

      double complex hankel2e(double, double complex)

- `huber`:

      double huber(double, double)

- `hyp0f1`:

      double complex hyp0f1(double, double complex)
      double hyp0f1(double, double)

- `hyp1f1`:

      double hyp1f1(double, double, double)
      double complex hyp1f1(double, double, double complex)

- `hyp2f1`:

      double hyp2f1(double, double, double, double)
      double complex hyp2f1(double, double, double, double complex)

- `hyperu`:

      double hyperu(double, double, double)

- `i0`:

      double i0(double)

- `i0e`:

      double i0e(double)

- `i1`:

      double i1(double)

- `i1e`:

      double i1e(double)

- `inv_boxcox`:

      double inv_boxcox(double, double)

- `inv_boxcox1p`:

      double inv_boxcox1p(double, double)

- `it2i0k0`:

      void it2i0k0(double, double *, double *)

- `it2j0y0`:

      void it2j0y0(double, double *, double *)

- `it2struve0`:

      double it2struve0(double)

- `itairy`:

      void itairy(double, double *, double *, double *, double *)

- `iti0k0`:

      void iti0k0(double, double *, double *)

- `itj0y0`:

      void itj0y0(double, double *, double *)

- `itmodstruve0`:

      double itmodstruve0(double)

- `itstruve0`:

      double itstruve0(double)

- `iv`:

      double complex iv(double, double complex)
      double iv(double, double)

- `ive`:

      double complex ive(double, double complex)
      double ive(double, double)

- `j0`:

      double j0(double)

- `j1`:

      double j1(double)

- `jv`:

      double complex jv(double, double complex)
      double jv(double, double)

- `jve`:

      double complex jve(double, double complex)
      double jve(double, double)

- `k0`:

      double k0(double)

- `k0e`:

      double k0e(double)

- `k1`:

      double k1(double)

- `k1e`:

      double k1e(double)

- `kei`:

      double kei(double)

- `keip`:

      double keip(double)

- `kelvin`:

      void kelvin(double, double complex *, double complex *, double complex *, double complex *)

- `ker`:

      double ker(double)

- `kerp`:

      double kerp(double)

- `kl_div`:

      double kl_div(double, double)

- `kn`:

      double kn(double, double)
      double kn(long, double)

- `kolmogi`:

      double kolmogi(double)

- `kolmogorov`:

      double kolmogorov(double)

- `kv`:

      double complex kv(double, double complex)
      double kv(double, double)

- `kve`:

      double complex kve(double, double complex)
      double kve(double, double)

- `log1p`:

      double complex log1p(double complex)
      double log1p(double)

- `log_expit`:

      double log_expit(double)
      float log_expit(float)
      long double log_expit(long double)

- `log_ndtr`:

      double log_ndtr(double)
      double complex log_ndtr(double complex)

- `loggamma`:

      double loggamma(double)
      double complex loggamma(double complex)

- `logit`:

      double logit(double)
      float logit(float)
      long double logit(long double)

- `lpmv`:

      double lpmv(double, double, double)

- `mathieu_a`:

      double mathieu_a(double, double)

- `mathieu_b`:

      double mathieu_b(double, double)

- `mathieu_cem`:

      void mathieu_cem(double, double, double, double *, double *)

- `mathieu_modcem1`:

      void mathieu_modcem1(double, double, double, double *, double *)

- `mathieu_modcem2`:

      void mathieu_modcem2(double, double, double, double *, double *)

- `mathieu_modsem1`:

      void mathieu_modsem1(double, double, double, double *, double *)

- `mathieu_modsem2`:

      void mathieu_modsem2(double, double, double, double *, double *)

- `mathieu_sem`:

      void mathieu_sem(double, double, double, double *, double *)

- `modfresnelm`:

      void modfresnelm(double, double complex *, double complex *)

- `modfresnelp`:

      void modfresnelp(double, double complex *, double complex *)

- `modstruve`:

      double modstruve(double, double)

- `nbdtr`:

      double nbdtr(double, double, double)
      double nbdtr(long, long, double)

- `nbdtrc`:

      double nbdtrc(double, double, double)
      double nbdtrc(long, long, double)

- `nbdtri`:

      double nbdtri(double, double, double)
      double nbdtri(long, long, double)

- `nbdtrik`:

      double nbdtrik(double, double, double)

- `nbdtrin`:

      double nbdtrin(double, double, double)

- `ncfdtr`:

      double ncfdtr(double, double, double, double)

- `ncfdtri`:

      double ncfdtri(double, double, double, double)

- `ncfdtridfd`:

      double ncfdtridfd(double, double, double, double)

- `ncfdtridfn`:

      double ncfdtridfn(double, double, double, double)

- `ncfdtrinc`:

      double ncfdtrinc(double, double, double, double)

- `nctdtr`:

      double nctdtr(double, double, double)

- `nctdtridf`:

      double nctdtridf(double, double, double)

- `nctdtrinc`:

      double nctdtrinc(double, double, double)

- `nctdtrit`:

      double nctdtrit(double, double, double)

- `ndtr`:

      double complex ndtr(double complex)
      double ndtr(double)

- `ndtri`:

      double ndtri(double)

- `nrdtrimn`:

      double nrdtrimn(double, double, double)

- `nrdtrisd`:

      double nrdtrisd(double, double, double)

- `obl_ang1`:

      void obl_ang1(double, double, double, double, double *, double *)

- `obl_ang1_cv`:

      void obl_ang1_cv(double, double, double, double, double, double *, double *)

- `obl_cv`:

      double obl_cv(double, double, double)

- `obl_rad1`:

      void obl_rad1(double, double, double, double, double *, double *)

- `obl_rad1_cv`:

      void obl_rad1_cv(double, double, double, double, double, double *, double *)

- `obl_rad2`:

      void obl_rad2(double, double, double, double, double *, double *)

- `obl_rad2_cv`:

      void obl_rad2_cv(double, double, double, double, double, double *, double *)

- `owens_t`:

      double owens_t(double, double)

- `pbdv`:

      void pbdv(double, double, double *, double *)

- `pbvv`:

      void pbvv(double, double, double *, double *)

- `pbwa`:

      void pbwa(double, double, double *, double *)

- `pdtr`:

      double pdtr(double, double)

- `pdtrc`:

      double pdtrc(double, double)

- `pdtri`:

      double pdtri(double, double)
      double pdtri(long, double)

- `pdtrik`:

      double pdtrik(double, double)

- `poch`:

      double poch(double, double)

- `powm1`:

      float powm1(float, float)
      double powm1(double, double)

- `pro_ang1`:

      void pro_ang1(double, double, double, double, double *, double *)

- `pro_ang1_cv`:

      void pro_ang1_cv(double, double, double, double, double, double *, double *)

- `pro_cv`:

      double pro_cv(double, double, double)

- `pro_rad1`:

      void pro_rad1(double, double, double, double, double *, double *)

- `pro_rad1_cv`:

      void pro_rad1_cv(double, double, double, double, double, double *, double *)

- `pro_rad2`:

      void pro_rad2(double, double, double, double, double *, double *)

- `pro_rad2_cv`:

      void pro_rad2_cv(double, double, double, double, double, double *, double *)

- `pseudo_huber`:

      double pseudo_huber(double, double)

- `psi`:

      double complex psi(double complex)
      double psi(double)

- `radian`:

      double radian(double, double, double)

- `rel_entr`:

      double rel_entr(double, double)

- `rgamma`:

      double complex rgamma(double complex)
      double rgamma(double)

- `round`:

      double round(double)

- `shichi`:

      void shichi(double complex, double complex *, double complex *)
      void shichi(double, double *, double *)

- `sici`:

      void sici(double complex, double complex *, double complex *)
      void sici(double, double *, double *)

- `sindg`:

      double sindg(double)

- `smirnov`:

      double smirnov(double, double)
      double smirnov(long, double)

- `smirnovi`:

      double smirnovi(double, double)
      double smirnovi(long, double)

- `spence`:

      double complex spence(double complex)
      double spence(double)

- `sph_harm`:

      double complex sph_harm(double, double, double, double)
      double complex sph_harm(long, long, double, double)

- `stdtr`:

      double stdtr(double, double)

- `stdtridf`:

      double stdtridf(double, double)

- `stdtrit`:

      double stdtrit(double, double)

- `struve`:

      double struve(double, double)

- `tandg`:

      double tandg(double)

- `tklmbda`:

      double tklmbda(double, double)

- `wofz`:

      double complex wofz(double complex)

- `wrightomega`:

      double complex wrightomega(double complex)
      double wrightomega(double)

- `xlog1py`:

      double xlog1py(double, double)
      double complex xlog1py(double complex, double complex)

- `xlogy`:

      double xlogy(double, double)
      double complex xlogy(double complex, double complex)

- `y0`:

      double y0(double)

- `y1`:

      double y1(double)

- `yn`:

      double yn(double, double)
      double yn(long, double)

- `yv`:

      double complex yv(double, double complex)
      double yv(double, double)

- `yve`:

      double complex yve(double, double complex)
      double yve(double, double)

- `zetac`:

      double zetac(double)

- `wright_bessel`:

      double wright_bessel(double, double, double)

- `log_wright_bessel`:

      double log_wright_bessel(double, double, double)

- `ndtri_exp`:

      double ndtri_exp(double)

## Custom functions

Some functions in `scipy.special` which are not ufuncs have custom Cython wrappers.

### Spherical Bessel functions

The optional `derivative` boolean argument is replaced with an optional Cython `bint`, leading to the following signatures.

- `spherical_jn`:

      double complex spherical_jn(Py_ssize_t, double complex)
      double complex spherical_jn(Py_ssize_t, double complex, bint)
      double spherical_jn(Py_ssize_t, double)
      double spherical_jn(Py_ssize_t, double, bint)

- `spherical_yn`:

      double complex spherical_yn(Py_ssize_t, double complex)
      double complex spherical_yn(Py_ssize_t, double complex, bint)
      double spherical_yn(Py_ssize_t, double)
      double spherical_yn(Py_ssize_t, double, bint)

- `spherical_in`:

      double complex spherical_in(Py_ssize_t, double complex)
      double complex spherical_in(Py_ssize_t, double complex, bint)
      double spherical_in(Py_ssize_t, double)
      double spherical_in(Py_ssize_t, double, bint)

- `spherical_kn`:

      double complex spherical_kn(Py_ssize_t, double complex)
      double complex spherical_kn(Py_ssize_t, double complex, bint)
      double spherical_kn(Py_ssize_t, double)
      double spherical_kn(Py_ssize_t, double, bint)