added local extrema of Bessel Y functions

data/Local_extrema/Local_extrema_of_Bessel_J_functions/generate.sage

@@ -27,17 +27,6 @@ for alpha in alpha_range:
 			max_digits = prec10,
 		).replace('?','')
 
-		'''
-		if alpha == 1/2:
-			#number = n*pi
-			if n == 1:
-				numbers_alpha[str(n)] = {
-					'number': number_str,
-					'equals': 'HREF{Pi}',
-				}
-				continue
-		'''
-
 		numbers_alpha[str(n)] = number_str
 
 	numbers[str(alpha)] = numbers_alpha

data/Local_extrema/Local_extrema_of_Bessel_Y_functions/collection.yaml

@@ -0,0 +1,56 @@
+ID: INPUT{id.yaml}
+
+Title: >
+  Local extrema of Bessel functions of the second kind $Y_\alpha$ 
+
+Definition: >
+  The list contains the first zeros of the derivative of 
+  Bessel functions of the second kind $Y_\alpha$.
+
+Parameters:
+  alpha:
+    display: $\alpha$
+    type: C
+  n:
+    type: Z
+    constraints: $n \geq 1$
+
+Comments:
+  comment-choice-of-alpha: >
+    This collection currently restricts to the important special case 
+    $\alpha \in \frac{1}{2}\mathbb{Z}_{\geq 0}$.
+  comment-maxima: >
+    Local maxima arise for odd $n$, local minima for even $n$.  
+  
+Formulas: 
+
+Programs: 
+
+References:
+
+Links:
+  mpmath: >
+    HREF{https://mpmath.org/}[mpmath] (Python library)
+  Wiki:
+    title: "Wikipedia: Bessel functions of the first kind"
+    url: https://en.wikipedia.org/wiki/Bessel_function#Bessel_functions_of_the_first_kind:_J%CE%B1
+
+Similar tables:
+
+Keywords:
+- maximum
+- minimum
+
+Tags:
+- local extrema
+- special functions
+
+Data properties:
+  type: R
+  complete: no
+  reliability: computed with mpmath CITE{mpmath}
+
+Display properties:
+  number-header: $n$<sup>th</sup> local extremum of $J_\alpha$
+
+Numbers: INPUT{numbers.yaml}

data/Local_extrema/Local_extrema_of_Bessel_Y_functions/generate.sage

@@ -0,0 +1,35 @@
+import yaml
+import os
+import mpmath
+from utils.utils import numbers_to_yaml
+from utils.utils import real_interval_to_sage_string
+
+
+path = 'data/Local_extrema/Local_extrema_of_Bessel_Y_functions/'
+
+prec10 = 100 #relative precision in base 10
+
+mpmath.mp.dps = prec10 * 1.5
+alpha_range = [a/2 for a in [0..20]] #order of Bessel Y-function
+n_range = [1..50] #index of zero of Y_alpha
+
+RIFprec = RealIntervalField(prec10 * 3.4 * 2)
+
+numbers = {}
+for alpha in alpha_range:
+	print("alpha:",alpha)
+	numbers_alpha = {}
+
+	for n in n_range:
+		number = mpmath.mp.besselyzero(alpha,n,derivative=1)
+		number_str = real_interval_to_sage_string(
+			RIFprec(number),
+			max_digits = prec10,
+		).replace('?','')
+
+		numbers_alpha[str(n)] = number_str
+
+	numbers[str(alpha)] = numbers_alpha
+
+filename = os.path.join(path, 'numbers.yaml')
+yaml.dump(numbers, stream = open(filename, 'w'), sort_keys = False)