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Scientific Arts

Pade

•Functions and parameters contained in this package:

In[75]:=

RadarPackageFunctions[PadeMethod, 3]

Out[75]//DisplayForm=

[Graphics:HTMLFiles/index_2.gif]

•Package functions and their basic documentation along with simple examples

•AiryAiPrimeZeroSeed

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In[1]:=

AiryAiPrimeZeroSeed[s]

Out[1]=

-1/4 (3 π)^(2/3) (-3 + 4 s)^(2/3) (1 - 373333542342656/(43046721 π^10 (-3 + 4 s)^10) ... (295245 π^6 (-3 + 4 s)^6) + 4480/(729 π^4 (-3 + 4 s)^4) - 28/(27 π^2 (-3 + 4 s)^2))

•AiryAiPrimeZeros

[Graphics:HTMLFiles/index_6.gif]

In[2]:=

Options[AiryAiPrimeZeros]

Out[2]=

{MaxIterations -> 50, AccuracyGoal -> 25, WorkingPrecision -> 40}

In[3]:=

AiryAiPrimeZeros[10]

Out[3]=

{-1.0187929716474710890173247833997438242182054411958599`40, -3.248197582179836537875423770775 ... 372165224056387347557208490892011`40, -12.3847883718457473254933392353826241009923701945945251`40}

•AiryAiZeroSeed

[Graphics:HTMLFiles/index_11.gif]

In[4]:=

AiryAiZeroSeed[s]

Out[4]=

-1/4 (3 π)^(2/3) (-1 + 4 s)^(2/3) (1 + 2660361779200000/(301327047 π^10 (-1 + 4 s)^1 ... /(59049 π^6 (-1 + 4 s)^6) - 5120/(729 π^4 (-1 + 4 s)^4) + 20/(27 π^2 (-1 + 4 s)^2))

•AiryAiZeros

[Graphics:HTMLFiles/index_14.gif]

In[5]:=

AiryAiZeros[10]

Out[5]=

{-2.3381074104597670384891972524467354406385400847440719`40, -4.087949444130970616636988701457 ... 063649029305843155778862321016737`40, -12.8287767528657572004067294072418244773864157423502418`40}

•AiryBiComplexZeroSeed

[Graphics:HTMLFiles/index_17.gif]

In[6]:=

AiryBiComplexZeroSeed[s]

Out[6]=

e^(i π)/3 (1 + 162375596875/(334430208 (3/8 π (-1 + 4 s) + 3/4 i Log[2])^10) - 10805 ... 4) + 5/(48 (3/8 π (-1 + 4 s) + 3/4 i Log[2])^2)) (3/8 π (-1 + 4 s) + 3/4 i Log[2])^(2/3)

•AiryBiComplexZeros

[Graphics:HTMLFiles/index_20.gif]

In[7]:=

AiryBiComplexZeros[10]

Out[7]=

{0.9775448867316206859469927060310129114279517764998865`39.7689 + 2.14129070603874457574913922 ... 354241241053158610901`39.8438 + 11.1585812267602532699699816892380151029697191558561056`40.0899 i}

•AiryBiPrimeComplexZeroSeed

[Graphics:HTMLFiles/index_23.gif]

In[8]:=

AiryBiPrimeComplexZeroSeed[s]

Out[8]=

e^(i π)/3 (1 - 91145884361/(191102976 (3/8 π (-3 + 4 s) + 3/4 i Log[2])^10) + 186833 ... 4) - 7/(48 (3/8 π (-3 + 4 s) + 3/4 i Log[2])^2)) (3/8 π (-3 + 4 s) + 3/4 i Log[2])^(2/3)

•AiryBiPrimeComplexZeros

[Graphics:HTMLFiles/index_26.gif]

In[9]:=

AiryBiPrimeComplexZeros[10]

Out[9]=

{0.214947074537430567608832870562506051873052248901381`39.4331 + 1.100600143302797880647194137 ... 37360615408724888006047`39.8434 + 10.7749565407967967872872685787053777656320111476370385`40.09 i}

•AiryBiPrimeZeroSeed

[Graphics:HTMLFiles/index_29.gif]

In[11]:=

AiryBiPrimeZeroSeed[12]

Out[11]=

-1/4 (1 - 373333542342656/(2264220170197882322719329 π^10) + 306108350464/(18981440992219 ... (3182509429810605 π^6) + 4480/(3557287449 π^4) - 28/(59643 π^2)) (141 π)^(2/3)

•AiryBiPrimeZeros

[Graphics:HTMLFiles/index_32.gif]

In[12]:=

AiryBiPrimeZeros[10]

Out[12]=

{-2.2944396826141232466224586737691028290784894670106107`40, -4.073155089071828215552368515092 ... 015696662788401862077978645529024`40, -12.8272583091772176401858251587417263226239863200140415`40}

•AiryBiZeroSeed

[Graphics:HTMLFiles/index_35.gif]

In[13]:=

AiryBiZeroSeed[12]

Out[13]=

-9/4 (1 + 851315769344/(3283320147121855771875 π^10) - 708161536/(300257900971363125 ` ... 157952/(3922632451125 π^6) - 1024/(597871125 π^4) + 4/(10935 π^2)) (5 π)^(2/3)

•AiryBiZeros

[Graphics:HTMLFiles/index_38.gif]

In[14]:=

AiryBiZeros[10]

Out[14]=

{-1.1737132227091279249199799624739021045436463781704681`40, -3.271093302836352715680228240166 ... 234649247328196719482538148333143`40, -12.3864171385827387455619015028632809482597999468244354`40}

In[15]:=

AiryBiZeros[{5, 10}]

Out[15]=

{-7.3767620793677637135999593304425412220915173224112895`40, -8.491948846509388013448039492809 ... 234649247328196719482538148333143`40, -12.3864171385827387455619015028632809482597999468244354`40}

•AiryComplexZerosWrite

[Graphics:HTMLFiles/index_43.gif]

•AiryZerosInfinity

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•AiryZerosWrite

[Graphics:HTMLFiles/index_45.gif]

•AiryZerosZero

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•MakeAiryZerosInfinity

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In[16]:=

Options[MakeAiryZerosInfinity]

Out[16]=

{AccuracyGoal -> Automatic, Compiled -> True, DampingFactor -> 1, Jacobian -> Automatic, MaxIterations -> 25, WorkingPrecision -> 60}

In[17]:=

MakeAiryZerosInfinity[10]

Out[17]=

{2.338107410459767038489197252446735440638540145672387852483854437213667999`60, 4.087949444130 ... 538642911432244`60, 12.82877675286575720040672940724182447738641559957341994148696675195607884`60}

In[18]:=

AiryAiZeros[10]

Out[18]=

{-2.3381074104597670384891972524467354406385400847440719`40, -4.087949444130970616636988701457 ... 063649029305843155778862321016737`40, -12.8287767528657572004067294072418244773864157423502418`40}

•MakeAiryZerosZero

[Graphics:HTMLFiles/index_54.gif]

•MakePadeCompiledFiles

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•MakePadeCompiled

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In[19]:=

MakePadeCompiled[3, q, 2, 16]

Out[19]=

CompiledFunction[{SpecialPadeq}, Block[{$2134, $2136}, $2134 = SpecialPadeq^2 ; $2136 = Specia ... 058850649` i) $2134 + (0.10974258542506193` + 2.489017221315161`*^-16 i) $2136)], -CompiledCode-]

•MakePadeFile

[Graphics:HTMLFiles/index_59.gif]

•MakePade

[Graphics:HTMLFiles/index_60.gif]

In[20]:=

MakePade[3, q, 2, 16]

Out[20]=

((1.6240987910899183` - 2.81302162267893` i) + (1.5996518720449047` + 2.7706783168044495` i) ... 52779669` + 0.3807541058850649` i) q^2 + (0.10974258542506193` + 2.489017221315161`*^-16 i) q^3)

•PadeMethod

[Graphics:HTMLFiles/index_63.gif]

•tlInfinity

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•tlSeriesInfinity

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In[21]:=

tlSeriesInfinity[5, q]

Out[21]=

1/(4 q^4) + 1/q + tlInfinity + tlInfinity/(3 q^3) + tlInfinity^2/(5 q^5)

•tlSeriesZero

[Graphics:HTMLFiles/index_68.gif]

In[22]:=

tlSeriesZero[5, q]

Out[22]=

q^4 (-5/(8 tlZero^7) - 7/(12 tlZero^4)) + q^5 (7/(8 tlZero^9) + 21/(20 tlZero^6) + 1/(5 tlZero^3)) + q^3 (1/(2 tlZero^5) + 1/(3 tlZero^2)) - q^2/(2 tlZero^3) + q/tlZero + tlZero

•tlZero

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