Confluent Hypergeometric Functions - 13.9 Zeros

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
13.9.E1	${\displaystyle{\displaystyle p(a,b)=\left\lceil-a\right\rceil}}$ p(a,b) = \ceiling{-a}	${\displaystyle{\displaystyle a<0,b\geq 0}}$	p(a , b) = ceil(- a)	p[a , b] == Ceiling[- a]	Failure	Failure	Failed [90 / 90] Result: (.8660254040+.5000000000*I)*(-1.500000000, 1.500000000)-2. Test Values: {a = -3/2, b = 3/2, p = 1/2*3^(1/2)+1/2*I} Result: (-.5000000000+.8660254040*I)*(-1.500000000, 1.500000000)-2. Test Values: {a = -3/2, b = 3/2, p = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Error
13.9.E2	${\displaystyle{\displaystyle p(a,b)=0}}$ p(a,b) = 0	${\displaystyle{\displaystyle a\geq 0,b\geq 0}}$	p(a , b) = 0	p[a , b] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
13.9.E3	${\displaystyle{\displaystyle p(a,b)=1}}$ p(a,b) = 1	${\displaystyle{\displaystyle a\geq 0,-1<b,b<0}}$	p(a , b) = 1	p[a , b] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
13.9.E4	${\displaystyle{\displaystyle p(a,b)=\left\lfloor-\tfrac{1}{2}b\right\rfloor-\left\lfloor-\tfrac{1}{2}(b+1)\right\rfloor}}$ p(a,b) = \floor{-\tfrac{1}{2}b}-\floor{-\tfrac{1}{2}(b+1)}	${\displaystyle{\displaystyle a\geq 0,b\leq-1}}$	p(a , b) = floor(-(1)/(2)*b)- floor(-(1)/(2)*(b + 1))	p[a , b] == Floor[-Divide[1,2]*b]- Floor[-Divide[1,2]*(b + 1)]	Failure	Failure	Error	Error
13.9.E5	${\displaystyle{\displaystyle p(a,b)=\left\lceil-a\right\rceil-\left\lceil-b\right\rceil}}$ p(a,b) = \ceiling{-a}-\ceiling{-b}	${\displaystyle{\displaystyle\left\lceil-a\right\rceil\geq\left\lceil-b\right\rceil,a<0,b<0}}$	p(a , b) = ceil(- a)- ceil(- b)	p[a , b] == Ceiling[- a]- Ceiling[- b]	Failure	Failure	Error	Error
13.9.E6	${\displaystyle{\displaystyle p(a,b)=\left\lfloor\tfrac{1}{2}\left(\left\lceil-b\right\rceil-\left\lceil-a\right\rceil+1\right)\right\rfloor-\left\lfloor\tfrac{1}{2}\left(\left\lceil-b\right\rceil-\left\lceil-a\right\rceil\right)\right\rfloor}}$ p(a,b) = \floor{\tfrac{1}{2}\left(\ceiling{-b}-\ceiling{-a}+1\right)}-\floor{\tfrac{1}{2}\left(\ceiling{-b}-\ceiling{-a}\right)}	${\displaystyle{\displaystyle\left\lceil-b\right\rceil>\left\lceil-a\right\rceil,\left\lceil-a\right\rceil>0}}$	p(a , b) = floor((1)/(2)*(ceil(- b)- ceil(- a)+ 1))- floor((1)/(2)*(ceil(- b)- ceil(- a)))	p[a , b] == Floor[Divide[1,2]*(Ceiling[- b]- Ceiling[- a]+ 1)]- Floor[Divide[1,2]*(Ceiling[- b]- Ceiling[- a])]	Failure	Failure	Failed [20 / 20] Result: (.8660254040+.5000000000*I)*(-.5000000000, -1.500000000)-1. Test Values: {a = -1/2, b = -3/2, p = 1/2*3^(1/2)+1/2*I} Result: (-.5000000000+.8660254040*I)*(-.5000000000, -1.500000000)-1. Test Values: {a = -1/2, b = -3/2, p = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Error
13.9.E11	${\displaystyle{\displaystyle T(a,b)=\left\lfloor-a\right\rfloor+1}}$ T(a,b) = \floor{-a}+1	${\displaystyle{\displaystyle a<0,\Gamma\left(a\right)\Gamma\left(a-b+1\right)>0}}$	T(a , b) = floor(- a)+ 1	T[a , b] == Floor[- a]+ 1	Failure	Failure	Error	Error
13.9.E12	${\displaystyle{\displaystyle T(a,b)=\left\lfloor-a\right\rfloor}}$ T(a,b) = \floor{-a}	${\displaystyle{\displaystyle a<0,\Gamma\left(a\right)\Gamma\left(a-b+1\right)<0}}$	T(a , b) = floor(- a)	T[a , b] == Floor[- a]	Failure	Failure	Error	Error
13.9.E13	${\displaystyle{\displaystyle T(a,b)=0}}$ T(a,b) = 0	${\displaystyle{\displaystyle a>0}}$	T(a , b) = 0	T[a , b] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
13.9.E14	${\displaystyle{\displaystyle P(a,b)=\left\lceil b-a-1\right\rceil}}$ P(a,b) = \ceiling{b-a-1}	${\displaystyle{\displaystyle a+1<b}}$	P(a , b) = ceil(b - a - 1)	P[a , b] == Ceiling[b - a - 1]	Failure	Failure	Failed [100 / 100] Result: (.8660254040+.5000000000*I)*(-1.500000000, 1.500000000)-2. Test Values: {P = 1/2*3^(1/2)+1/2*I, a = -3/2, b = 3/2} Result: (.8660254040+.5000000000*I)*(-1.500000000, .5000000000)-1. Test Values: {P = 1/2*3^(1/2)+1/2*I, a = -3/2, b = 1/2} ... skip entries to safe data	Error
13.9.E15	${\displaystyle{\displaystyle P(a,b)=0}}$ P(a,b) = 0	${\displaystyle{\displaystyle a+1\geq b}}$	P(a , b) = 0	P[a , b] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-