From 9f369d3c8d4db0d7265cb6318407b6f0e7badffb Mon Sep 17 00:00:00 2001 From: Yaakov Selkowitz Date: Thu, 30 Nov 2017 02:51:13 -0600 Subject: [PATCH] mathfp: remove TRAD_SYNOPSIS Signed-off-by: Yaakov Selkowitz --- newlib/libm/mathfp/e_acosh.c | 10 +-------- newlib/libm/mathfp/e_atanh.c | 10 +-------- newlib/libm/mathfp/e_hypot.c | 9 +------- newlib/libm/mathfp/e_remainder.c | 9 +------- newlib/libm/mathfp/er_lgamma.c | 25 +---------------------- newlib/libm/mathfp/s_acos.c | 12 +---------- newlib/libm/mathfp/s_asine.c | 22 +------------------- newlib/libm/mathfp/s_asinh.c | 10 +-------- newlib/libm/mathfp/s_atan.c | 10 +-------- newlib/libm/mathfp/s_atan2.c | 12 +---------- newlib/libm/mathfp/s_atangent.c | 19 +---------------- newlib/libm/mathfp/s_cosh.c | 10 +-------- newlib/libm/mathfp/s_erf.c | 16 +-------------- newlib/libm/mathfp/s_exp.c | 10 +-------- newlib/libm/mathfp/s_fabs.c | 10 +-------- newlib/libm/mathfp/s_floor.c | 13 +----------- newlib/libm/mathfp/s_fmod.c | 10 +-------- newlib/libm/mathfp/s_frexp.c | 13 +----------- newlib/libm/mathfp/s_ldexp.c | 13 +----------- newlib/libm/mathfp/s_log10.c | 10 +-------- newlib/libm/mathfp/s_logarithm.c | 16 +-------------- newlib/libm/mathfp/s_pow.c | 10 +-------- newlib/libm/mathfp/s_sine.c | 14 +------------ newlib/libm/mathfp/s_sineh.c | 15 +------------- newlib/libm/mathfp/s_sqrt.c | 7 +------ newlib/libm/mathfp/s_tan.c | 11 +--------- newlib/libm/mathfp/s_tanh.c | 11 +--------- newlib/libm/mathfp/w_jn.c | 35 +------------------------------- 28 files changed, 28 insertions(+), 344 deletions(-) diff --git a/newlib/libm/mathfp/e_acosh.c b/newlib/libm/mathfp/e_acosh.c index 7b199c5d9..0ad0f0611 100644 --- a/newlib/libm/mathfp/e_acosh.c +++ b/newlib/libm/mathfp/e_acosh.c @@ -10,19 +10,11 @@ acosh INDEX acoshf -ANSI_SYNOPSIS +SYNOPSIS #include double acosh(double <[x]>); float acoshf(float <[x]>); -TRAD_SYNOPSIS - #include - double acosh(<[x]>) - double <[x]>; - - float acoshf(<[x]>) - float <[x]>; - DESCRIPTION <> calculates the inverse hyperbolic cosine of <[x]>. <> is defined as diff --git a/newlib/libm/mathfp/e_atanh.c b/newlib/libm/mathfp/e_atanh.c index fb233e5d4..072c44607 100644 --- a/newlib/libm/mathfp/e_atanh.c +++ b/newlib/libm/mathfp/e_atanh.c @@ -21,19 +21,11 @@ INDEX INDEX atanhf -ANSI_SYNOPSIS +SYNOPSIS #include double atanh(double <[x]>); float atanhf(float <[x]>); -TRAD_SYNOPSIS - #include - double atanh(<[x]>) - double <[x]>; - - float atanhf(<[x]>) - float <[x]>; - DESCRIPTION <> calculates the inverse hyperbolic tangent of <[x]>. diff --git a/newlib/libm/mathfp/e_hypot.c b/newlib/libm/mathfp/e_hypot.c index 713aa77c2..1a59afcde 100644 --- a/newlib/libm/mathfp/e_hypot.c +++ b/newlib/libm/mathfp/e_hypot.c @@ -19,18 +19,11 @@ INDEX INDEX hypotf -ANSI_SYNOPSIS +SYNOPSIS #include double hypot(double <[x]>, double <[y]>); float hypotf(float <[x]>, float <[y]>); -TRAD_SYNOPSIS - double hypot(<[x]>, <[y]>) - double <[x]>, <[y]>; - - float hypotf(<[x]>, <[y]>) - float <[x]>, <[y]>; - DESCRIPTION <> calculates the Euclidean distance @tex diff --git a/newlib/libm/mathfp/e_remainder.c b/newlib/libm/mathfp/e_remainder.c index 02a714d5b..a80706cc1 100644 --- a/newlib/libm/mathfp/e_remainder.c +++ b/newlib/libm/mathfp/e_remainder.c @@ -19,18 +19,11 @@ INDEX INDEX remainderf -ANSI_SYNOPSIS +SYNOPSIS #include double remainder(double <[x]>, double <[y]>); float remainderf(float <[x]>, float <[y]>); -TRAD_SYNOPSIS - #include - double remainder(<[x]>,<[y]>) - double <[x]>, <[y]>; - float remainderf(<[x]>,<[y]>) - float <[x]>, <[y]>; - DESCRIPTION <> and <> find the remainder of <[x]>/<[y]>; this value is in the range -<[y]>/2 .. +<[y]>/2. diff --git a/newlib/libm/mathfp/er_lgamma.c b/newlib/libm/mathfp/er_lgamma.c index fd49c252e..915dac7d0 100644 --- a/newlib/libm/mathfp/er_lgamma.c +++ b/newlib/libm/mathfp/er_lgamma.c @@ -34,7 +34,7 @@ lgamma_r INDEX lgammaf_r -ANSI_SYNOPSIS +SYNOPSIS #include double gamma(double <[x]>); float gammaf(float <[x]>); @@ -45,29 +45,6 @@ float gammaf_r(float <[x]>, int *<[signgamp]>); double lgamma_r(double <[x]>, int *<[signgamp]>); float lgammaf_r(float <[x]>, int *<[signgamp]>); -TRAD_SYNOPSIS -#include -double gamma(<[x]>) -double <[x]>; -float gammaf(<[x]>) -float <[x]>; -double lgamma(<[x]>) -double <[x]>; -float lgammaf(<[x]>) -float <[x]>; -double gamma_r(<[x]>, <[signgamp]>) -double <[x]>; -int <[signgamp]>; -float gammaf_r(<[x]>, <[signgamp]>) -float <[x]>; -int <[signgamp]>; -double lgamma_r(<[x]>, <[signgamp]>) -double <[x]>; -int <[signgamp]>; -float lgammaf_r(<[x]>, <[signgamp]>) -float <[x]>; -int <[signgamp]>; - DESCRIPTION <> calculates @tex diff --git a/newlib/libm/mathfp/s_acos.c b/newlib/libm/mathfp/s_acos.c index 051afea72..d66a5cd26 100644 --- a/newlib/libm/mathfp/s_acos.c +++ b/newlib/libm/mathfp/s_acos.c @@ -10,21 +10,11 @@ INDEX INDEX acosf -ANSI_SYNOPSIS +SYNOPSIS #include double acos(double <[x]>); float acosf(float <[x]>); -TRAD_SYNOPSIS - #include - double acos(<[x]>) - double <[x]>; - - float acosf(<[x]>) - float <[x]>; - - - DESCRIPTION <> computes the inverse cosine (arc cosine) of the input value. diff --git a/newlib/libm/mathfp/s_asine.c b/newlib/libm/mathfp/s_asine.c index 89a2bed5e..3212862b8 100644 --- a/newlib/libm/mathfp/s_asine.c +++ b/newlib/libm/mathfp/s_asine.c @@ -24,7 +24,7 @@ INDEX INDEX asinef -ANSI_SYNOPSIS +SYNOPSIS #include double asine(double <[x]>); float asinef(float <[x]>); @@ -33,26 +33,6 @@ ANSI_SYNOPSIS double acos(double <[x]>); float acosf(float <[x]>); -TRAD_SYNOPSIS - #include - double asine(<[x]>); - double <[x]>; - - float asinef(<[x]>); - float <[x]>; - - double asin(<[x]>) - double <[x]>; - - float asinf(<[x]>) - float <[x]>; - - double acos(<[x]>) - double <[x]>; - - float acosf(<[x]>) - float <[x]>; - DESCRIPTION <> computes the inverse sine or cosine of the argument <[x]>. diff --git a/newlib/libm/mathfp/s_asinh.c b/newlib/libm/mathfp/s_asinh.c index d70cc61db..cedc941a3 100644 --- a/newlib/libm/mathfp/s_asinh.c +++ b/newlib/libm/mathfp/s_asinh.c @@ -20,19 +20,11 @@ INDEX INDEX asinhf -ANSI_SYNOPSIS +SYNOPSIS #include double asinh(double <[x]>); float asinhf(float <[x]>); -TRAD_SYNOPSIS - #include - double asinh(<[x]>) - double <[x]>; - - float asinhf(<[x]>) - float <[x]>; - DESCRIPTION <> calculates the inverse hyperbolic sine of <[x]>. <> is defined as diff --git a/newlib/libm/mathfp/s_atan.c b/newlib/libm/mathfp/s_atan.c index a5a818979..0dd339474 100644 --- a/newlib/libm/mathfp/s_atan.c +++ b/newlib/libm/mathfp/s_atan.c @@ -10,19 +10,11 @@ INDEX INDEX atanf -ANSI_SYNOPSIS +SYNOPSIS #include double atan(double <[x]>); float atanf(float <[x]>); -TRAD_SYNOPSIS - #include - double atan(<[x]>); - double <[x]>; - - float atanf(<[x]>); - float <[x]>; - DESCRIPTION <> computes the inverse tangent (arc tangent) of the input value. diff --git a/newlib/libm/mathfp/s_atan2.c b/newlib/libm/mathfp/s_atan2.c index 60034b3ad..00121db4b 100644 --- a/newlib/libm/mathfp/s_atan2.c +++ b/newlib/libm/mathfp/s_atan2.c @@ -10,21 +10,11 @@ INDEX INDEX atan2f -ANSI_SYNOPSIS +SYNOPSIS #include double atan2(double <[y]>,double <[x]>); float atan2f(float <[y]>,float <[x]>); -TRAD_SYNOPSIS - #include - double atan2(<[y]>,<[x]>); - double <[y]>; - double <[x]>; - - float atan2f(<[y]>,<[x]>); - float <[y]>; - float <[x]>; - DESCRIPTION <> computes the inverse tangent (arc tangent) of <[y]>/<[x]>. diff --git a/newlib/libm/mathfp/s_atangent.c b/newlib/libm/mathfp/s_atangent.c index 0a7c4d2f8..cd9db2dcd 100644 --- a/newlib/libm/mathfp/s_atangent.c +++ b/newlib/libm/mathfp/s_atangent.c @@ -20,30 +20,13 @@ INDEX INDEX atanf -ANSI_SYNOPSIS +SYNOPSIS #include double atan(double <[x]>); float atan(float <[x]>); double atan2(double <[y]>,double <[x]>); float atan2f(float <[y]>,float <[x]>); -TRAD_SYNOPSIS - #include - double atan2(<[y]>,<[x]>); - double <[y]>; - double <[x]>; - - float atan2f(<[y]>,<[x]>); - float <[y]>; - float <[x]>; - - #include - double atan(<[x]>); - double <[x]>; - - float atanf(<[x]>); - float <[x]>; - DESCRIPTION <> computes the inverse tangent (arc tangent) of y / x. diff --git a/newlib/libm/mathfp/s_cosh.c b/newlib/libm/mathfp/s_cosh.c index f91411037..552e5ee5c 100644 --- a/newlib/libm/mathfp/s_cosh.c +++ b/newlib/libm/mathfp/s_cosh.c @@ -6,19 +6,11 @@ FUNCTION <>, <>---hyperbolic cosine -ANSI_SYNOPSIS +SYNOPSIS #include double cosh(double <[x]>); float coshf(float <[x]>); -TRAD_SYNOPSIS - #include - double cosh(<[x]>); - double <[x]>; - - float coshf(<[x]>); - float <[x]>; - DESCRIPTION <> computes the hyperbolic cosine of the argument <[x]>. diff --git a/newlib/libm/mathfp/s_erf.c b/newlib/libm/mathfp/s_erf.c index 2d8faa3d8..514da7464 100644 --- a/newlib/libm/mathfp/s_erf.c +++ b/newlib/libm/mathfp/s_erf.c @@ -23,26 +23,12 @@ INDEX INDEX erfcf -ANSI_SYNOPSIS +SYNOPSIS #include double erf(double <[x]>); float erff(float <[x]>); double erfc(double <[x]>); float erfcf(float <[x]>); -TRAD_SYNOPSIS - #include - - double erf(<[x]>) - double <[x]>; - - float erff(<[x]>) - float <[x]>; - - double erfc(<[x]>) - double <[x]>; - - float erfcf(<[x]>) - float <[x]>; DESCRIPTION <> calculates an approximation to the ``error function'', diff --git a/newlib/libm/mathfp/s_exp.c b/newlib/libm/mathfp/s_exp.c index e70699b06..362b8b079 100644 --- a/newlib/libm/mathfp/s_exp.c +++ b/newlib/libm/mathfp/s_exp.c @@ -15,19 +15,11 @@ INDEX INDEX expf -ANSI_SYNOPSIS +SYNOPSIS #include double exp(double <[x]>); float expf(float <[x]>); -TRAD_SYNOPSIS - #include - double exp(<[x]>); - double <[x]>; - - float expf(<[x]>); - float <[x]>; - DESCRIPTION <> and <> calculate the exponential of <[x]>, that is, @ifnottex diff --git a/newlib/libm/mathfp/s_fabs.c b/newlib/libm/mathfp/s_fabs.c index 9e1d75eb3..3d6d83889 100644 --- a/newlib/libm/mathfp/s_fabs.c +++ b/newlib/libm/mathfp/s_fabs.c @@ -9,19 +9,11 @@ INDEX INDEX fabsf -ANSI_SYNOPSIS +SYNOPSIS #include double fabs(double <[x]>); float fabsf(float <[x]>); -TRAD_SYNOPSIS - #include - double fabs(<[x]>) - double <[x]>; - - float fabsf(<[x]>) - float <[x]>; - DESCRIPTION <> and <> calculate @tex diff --git a/newlib/libm/mathfp/s_floor.c b/newlib/libm/mathfp/s_floor.c index 0dbc207f3..ebdb9a7b3 100644 --- a/newlib/libm/mathfp/s_floor.c +++ b/newlib/libm/mathfp/s_floor.c @@ -13,24 +13,13 @@ INDEX INDEX ceilf -ANSI_SYNOPSIS +SYNOPSIS #include double floor(double <[x]>); float floorf(float <[x]>); double ceil(double <[x]>); float ceilf(float <[x]>); -TRAD_SYNOPSIS - #include - double floor(<[x]>) - double <[x]>; - float floorf(<[x]>) - float <[x]>; - double ceil(<[x]>) - double <[x]>; - float ceilf(<[x]>) - float <[x]>; - DESCRIPTION <> and <> find @tex diff --git a/newlib/libm/mathfp/s_fmod.c b/newlib/libm/mathfp/s_fmod.c index 19bba9c18..d878f009c 100644 --- a/newlib/libm/mathfp/s_fmod.c +++ b/newlib/libm/mathfp/s_fmod.c @@ -20,19 +20,11 @@ fmod INDEX fmodf -ANSI_SYNOPSIS +SYNOPSIS #include double fmod(double <[x]>, double <[y]>); float fmodf(float <[x]>, float <[y]>); -TRAD_SYNOPSIS -#include -double fmod(<[x]>, <[y]>); -double (<[x]>, <[y]>); - -float fmodf(<[x]>, <[y]>); -float (<[x]>, <[y]>); - DESCRIPTION The <> and <> functions compute the floating-point remainder of <[x]>/<[y]> (<[x]> modulo <[y]>). diff --git a/newlib/libm/mathfp/s_frexp.c b/newlib/libm/mathfp/s_frexp.c index 54fa336c8..c0990df5f 100644 --- a/newlib/libm/mathfp/s_frexp.c +++ b/newlib/libm/mathfp/s_frexp.c @@ -9,22 +9,11 @@ INDEX INDEX frexpf -ANSI_SYNOPSIS +SYNOPSIS #include double frexp(double <[val]>, int *<[exp]>); float frexpf(float <[val]>, int *<[exp]>); -TRAD_SYNOPSIS - #include - double frexp(<[val]>, <[exp]>) - double <[val]>; - int *<[exp]>; - - float frexpf(<[val]>, <[exp]>) - float <[val]>; - int *<[exp]>; - - DESCRIPTION All nonzero, normal numbers can be described as <[m]> * 2**<[p]>. <> represents the double <[val]> as a mantissa <[m]> diff --git a/newlib/libm/mathfp/s_ldexp.c b/newlib/libm/mathfp/s_ldexp.c index 6da41284b..6971af697 100644 --- a/newlib/libm/mathfp/s_ldexp.c +++ b/newlib/libm/mathfp/s_ldexp.c @@ -10,22 +10,11 @@ INDEX INDEX ldexpf -ANSI_SYNOPSIS +SYNOPSIS #include double ldexp(double <[val]>, int <[exp]>); float ldexpf(float <[val]>, int <[exp]>); -TRAD_SYNOPSIS - #include - - double ldexp(<[val]>, <[exp]>) - double <[val]>; - int <[exp]>; - - float ldexpf(<[val]>, <[exp]>) - float <[val]>; - int <[exp]>; - DESCRIPTION <> calculates the value @ifnottex diff --git a/newlib/libm/mathfp/s_log10.c b/newlib/libm/mathfp/s_log10.c index 080cecd81..9491cff76 100644 --- a/newlib/libm/mathfp/s_log10.c +++ b/newlib/libm/mathfp/s_log10.c @@ -23,19 +23,11 @@ log10 INDEX log10f -ANSI_SYNOPSIS +SYNOPSIS #include double log10(double <[x]>); float log10f(float <[x]>); -TRAD_SYNOPSIS - #include - double log10(<[x]>) - double <[x]>; - - float log10f(<[x]>) - float <[x]>; - DESCRIPTION <> returns the base 10 logarithm of <[x]>. It is implemented as <) / log(10)>>. diff --git a/newlib/libm/mathfp/s_logarithm.c b/newlib/libm/mathfp/s_logarithm.c index 51e7f3066..977a6406d 100644 --- a/newlib/libm/mathfp/s_logarithm.c +++ b/newlib/libm/mathfp/s_logarithm.c @@ -20,27 +20,13 @@ INDEX INDEX log10f -ANSI_SYNOPSIS +SYNOPSIS #include double log(double <[x]>); float logf(float <[x]>); double log10(double <[x]>); float log10f(float <[x]>); -TRAD_SYNOPSIS - #include - double log(<[x]>); - double <[x]>; - - float logf(<[x]>); - float <[x]>; - - double log10(<[x]>); - double <[x]>; - - float log10f(<[x]>); - float <[x]>; - DESCRIPTION Return the natural or base 10 logarithm of <[x]>, that is, its logarithm base e (where e is the base of the natural system of logarithms, 2.71828@dots{}) or diff --git a/newlib/libm/mathfp/s_pow.c b/newlib/libm/mathfp/s_pow.c index 90d9d0b5f..5866dcd06 100644 --- a/newlib/libm/mathfp/s_pow.c +++ b/newlib/libm/mathfp/s_pow.c @@ -10,19 +10,11 @@ INDEX powf -ANSI_SYNOPSIS +SYNOPSIS #include double pow(double <[x]>, double <[y]>); float pow(float <[x]>, float <[y]>); -TRAD_SYNOPSIS - #include - double pow(<[x]>, <[y]>); - double <[x]>, <[y]>; - - float pow(<[x]>, <[y]>); - float <[x]>, <[y]>; - DESCRIPTION <> and <> calculate <[x]> raised to the exponent <[y]>. @tex diff --git a/newlib/libm/mathfp/s_sine.c b/newlib/libm/mathfp/s_sine.c index 9642f4a56..f8bf52952 100644 --- a/newlib/libm/mathfp/s_sine.c +++ b/newlib/libm/mathfp/s_sine.c @@ -18,25 +18,13 @@ INDEX cos INDEX cosf -ANSI_SYNOPSIS +SYNOPSIS #include double sin(double <[x]>); float sinf(float <[x]>); double cos(double <[x]>); float cosf(float <[x]>); -TRAD_SYNOPSIS - #include - double sin(<[x]>) - double <[x]>; - float sinf(<[x]>) - float <[x]>; - - double cos(<[x]>) - double <[x]>; - float cosf(<[x]>) - float <[x]>; - DESCRIPTION <> and <> compute (respectively) the sine and cosine of the argument <[x]>. Angles are specified in radians. diff --git a/newlib/libm/mathfp/s_sineh.c b/newlib/libm/mathfp/s_sineh.c index 6f5e208b0..581484ac1 100644 --- a/newlib/libm/mathfp/s_sineh.c +++ b/newlib/libm/mathfp/s_sineh.c @@ -20,25 +20,12 @@ INDEX INDEX coshf -ANSI_SYNOPSIS +SYNOPSIS #include double sinh(double <[x]>); float sinhf(float <[x]>); double cosh(double <[x]>); float coshf(float <[x]>); -TRAD_SYNOPSIS - #include - double sinh(<[x]>) - double <[x]>; - - float sinhf(<[x]>) - float <[x]>; - - double cosh(<[x]>) - double <[x]>; - - float coshf(<[x]>) - float <[x]>; DESCRIPTION <> and <> compute the hyperbolic sine or cosine diff --git a/newlib/libm/mathfp/s_sqrt.c b/newlib/libm/mathfp/s_sqrt.c index bafbb38b1..af3b1d85e 100644 --- a/newlib/libm/mathfp/s_sqrt.c +++ b/newlib/libm/mathfp/s_sqrt.c @@ -16,16 +16,11 @@ INDEX INDEX sqrtf -ANSI_SYNOPSIS +SYNOPSIS #include double sqrt(double <[x]>); float sqrtf(float <[x]>); -TRAD_SYNOPSIS - #include - double sqrt(<[x]>); - float sqrtf(<[x]>); - DESCRIPTION <> computes the positive square root of the argument. diff --git a/newlib/libm/mathfp/s_tan.c b/newlib/libm/mathfp/s_tan.c index 725aeec26..3910a4c49 100644 --- a/newlib/libm/mathfp/s_tan.c +++ b/newlib/libm/mathfp/s_tan.c @@ -16,20 +16,11 @@ tan INDEX tanf -ANSI_SYNOPSIS +SYNOPSIS #include double tan(double <[x]>); float tanf(float <[x]>); -TRAD_SYNOPSIS - #include - double tan(<[x]>) - double <[x]>; - - float tanf(<[x]>) - float <[x]>; - - DESCRIPTION <> computes the tangent of the argument <[x]>. Angles are specified in radians. diff --git a/newlib/libm/mathfp/s_tanh.c b/newlib/libm/mathfp/s_tanh.c index a19855e0b..7c92c1750 100644 --- a/newlib/libm/mathfp/s_tanh.c +++ b/newlib/libm/mathfp/s_tanh.c @@ -17,20 +17,11 @@ tanh INDEX tanhf -ANSI_SYNOPSIS +SYNOPSIS #include double tanh(double <[x]>); float tanhf(float <[x]>); -TRAD_SYNOPSIS - #include - double tanh(<[x]>) - double <[x]>; - - float tanhf(<[x]>) - float <[x]>; - - DESCRIPTION <> computes the hyperbolic tangent of diff --git a/newlib/libm/mathfp/w_jn.c b/newlib/libm/mathfp/w_jn.c index 14c2225f0..71ea4a095 100644 --- a/newlib/libm/mathfp/w_jn.c +++ b/newlib/libm/mathfp/w_jn.c @@ -40,7 +40,7 @@ yn INDEX ynf -ANSI_SYNOPSIS +SYNOPSIS #include double j0(double <[x]>); float j0f(float <[x]>); @@ -55,39 +55,6 @@ float y1f(float <[x]>); double yn(int <[n]>, double <[x]>); float ynf(int <[n]>, float <[x]>); -TRAD_SYNOPSIS -#include - -double j0(<[x]>) -double <[x]>; -float j0f(<[x]>) -float <[x]>; -double j1(<[x]>) -double <[x]>; -float j1f(<[x]>) -float <[x]>; -double jn(<[n]>, <[x]>) -int <[n]>; -double <[x]>; -float jnf(<[n]>, <[x]>) -int <[n]>; -float <[x]>; - -double y0(<[x]>) -double <[x]>; -float y0f(<[x]>) -float <[x]>; -double y1(<[x]>) -double <[x]>; -float y1f(<[x]>) -float <[x]>; -double yn(<[n]>, <[x]>) -int <[n]>; -double <[x]>; -float ynf(<[n]>, <[x]>) -int <[n]>; -float <[x]>; - DESCRIPTION The Bessel functions are a family of functions that solve the differential equation