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pi</plaintext> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP35019871d93ea43g0ga000046d2hcagi4370e32?MSPStoreType=image/gif&amp;s=57\' alt=\'pi\' title=\'pi\' width=\'9\' height=\'20\' /> </subpod> </pod> <pod title=\'Decimal approximation\' scanner=\'Numeric\' id=\'{&quot;Decimal approximation&quot;, {&quot;NumericScanner&quot;}}\' position=\'200\' error=\'false\' numsubpods=\'1\'> <subpod title=\'\'> <plaintext>3.1415926535897932384626433832795028841971693993751058209749...</plaintext> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP35119871d93ea43g0ga0000455bac815i44ff65?MSPStoreType=image/gif&amp;s=57\' alt=\'3.1415926535897932384626433832795028841971693993751058209749...\' title=\'3.1415926535897932384626433832795028841971693993751058209749...\' width=\'491\' height=\'20\' /> </subpod> <states count=\'1\'> <state name=\'More digits\' /> </states> </pod> <pod title=\'Property\' scanner=\'Numeric\' id=\'{&quot;Property&quot;, {&quot;NumericScanner&quot;}}\' position=\'300\' error=\'false\' numsubpods=\'1\'> <subpod title=\'\'> <plaintext>pi is a transcendental number</plaintext> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP35219871d93ea43g0ga00004d702a8e7dd39ai6?MSPStoreType=image/gif&amp;s=57\' alt=\'pi is a transcendental number\' title=\'pi is a transcendental number\' width=\'194\' height=\'20\' /> </subpod> </pod> <pod title=\'Continued fraction\' scanner=\'ContinuedFraction\' id=\'{&quot;Continued fraction&quot;, {&quot;ContinuedFractionScanner&quot;}}\' position=\'400\' error=\'false\' numsubpods=\'1\'> <subpod title=\'\'> <plaintext>[3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, ...]</plaintext> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP35319871d93ea43g0ga00002a1aib16efai1173?MSPStoreType=image/gif&amp;s=57\' alt=\'[3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, ...]\' title=\'[3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, ...]\' width=\'491\' height=\'20\' /> </subpod> <states count=\'2\'> <state name=\'Fraction form\' /> <state name=\'More terms\' /> </states> </pod> <pod title=\'Alternative representations\' scanner=\'MathematicalFunctionData\' id=\'{{&quot;AlternativeRepresentations&quot;, &quot;MathematicalFunctionIdentityData&quot;}, {&quot;MathematicalFunctionDataScanner&quot;}}\' position=\'500\' error=\'false\' numsubpods=\'3\'> <subpod title=\'\'> <plaintext>pi = 180 deg </plaintext> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP35419871d93ea43g0ga00001aad755c0hf6201b?MSPStoreType=image/gif&amp;s=57\' alt=\'pi = 180 deg \' title=\'pi = 180 deg \' width=\'61\' height=\'30\' /> </subpod> <subpod title=\'\'> <plaintext>pi = -i log(-1)</plaintext> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP35519871d93ea43g0ga00003e4ddi1f945eafc6?MSPStoreType=image/gif&amp;s=57\' alt=\'pi = -i log(-1)\' title=\'pi = -i log(-1)\' width=\'97\' height=\'30\' /> </subpod> <subpod title=\'\'> <plaintext>pi = 2 E(0)</plaintext> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP35619871d93ea43g0ga0000561b4i2419g83id3?MSPStoreType=image/gif&amp;s=57\' alt=\'pi = 2 E(0)\' title=\'pi = 2 E(0)\' width=\'67\' height=\'30\' /> </subpod> <states count=\'1\'> <state name=\'More\' /> </states> <infos count=\'4\'> <info text=\'E(m) is the complete elliptic integral of the second kind\'> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP35719871d93ea43g0ga000021d7chhg5b8ahhe7?MSPStoreType=image/gif&amp;s=57\' alt=\'E(m) is the complete elliptic integral of the second kind\' title=\'E(m) is the complete elliptic integral of the second kind\' width=\'350\' height=\'18\' /> <link url=\'http://reference.wolfram.com/mathematica/ref/EllipticE.html\' text=\'Documentation\' title=\'Mathematica\' /> <link url=\'http://functions.wolfram.com/EllipticIntegrals/EllipticE\' text=\'Properties\' title=\'Wolfram Functions Site\' /> <link url=\'http://mathworld.wolfram.com/CompleteEllipticIntegraloftheSecondKind.html\' text=\'Definition\' title=\'MathWorld\' /> </info> <info text=\'i is the imaginary unit\'> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP35819871d93ea43g0ga00004i7ca2cbf0ec1f7a?MSPStoreType=image/gif&amp;s=57\' alt=\'i is the imaginary unit\' title=\'i is the imaginary unit\' width=\'137\' height=\'18\' /> <link url=\'http://reference.wolfram.com/mathematica/ref/I.html\' text=\'Documentation\' title=\'Documentation\' /> <link url=\'http://mathworld.wolfram.com/i.html\' text=\'Definition\' title=\'MathWorld\' /> </info> <info text=\'log(x) is the natural logarithm\'> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP35919871d93ea43g0ga00005d59g13e459bfddb?MSPStoreType=image/gif&amp;s=57\' alt=\'log(x) is the natural logarithm\' title=\'log(x) is the natural logarithm\' width=\'192\' height=\'18\' /> <link url=\'http://reference.wolfram.com/mathematica/ref/Log.html\' text=\'Documentation\' title=\'Mathematica\' /> <link url=\'http://functions.wolfram.com/ElementaryFunctions/Log\' text=\'Properties\' title=\'Wolfram Functions Site\' /> <link url=\'http://mathworld.wolfram.com/NaturalLogarithm.html\' text=\'Definition\' title=\'MathWorld\' /> </info> <info> <link url=\'http://functions.wolfram.com/Constants/Pi/27/ShowAll.html\' text=\'More information\' /> </info> </infos> </pod> <pod title=\'Series representations\' scanner=\'MathematicalFunctionData\' id=\'{{&quot;SeriesRepresentations&quot;, &quot;MathematicalFunctionIdentityData&quot;}, {&quot;MathematicalFunctionDataScanner&quot;}}\' position=\'600\' error=\'false\' numsubpods=\'3\'> <subpod title=\'\'> <plaintext>pi = 4 sum_(k=0)^infinity(-1)^k/(2 k+1)</plaintext> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP36019871d93ea43g0ga000032ie35677c2b12a5?MSPStoreType=image/gif&amp;s=57\' alt=\'pi = 4 sum_(k=0)^infinity(-1)^k/(2 k+1)\' title=\'pi = 4 sum_(k=0)^infinity(-1)^k/(2 k+1)\' width=\'110\' height=\'57\' /> </subpod> <subpod title=\'\'> <plaintext>pi = -2+2 sum_(k=1)^infinity2^k/(2 k k)</plaintext> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP36119871d93ea43g0ga00004c1g0be822a420c8?MSPStoreType=image/gif&amp;s=57\' alt=\'pi = -2+2 sum_(k=1)^infinity2^k/(2 k k)\' title=\'pi = -2+2 sum_(k=1)^infinity2^k/(2 k k)\' width=\'139\' height=\'70\' /> </subpod> <subpod title=\'\'> <plaintext>pi = sum_(k=0)^infinity(50 k-6)/(2^k (3 k k))</plaintext> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP36219871d93ea43g0ga0000695g21a3ade92f1c?MSPStoreType=image/gif&amp;s=57\' alt=\'pi = sum_(k=0)^infinity(50 k-6)/(2^k (3 k k))\' title=\'pi = sum_(k=0)^infinity(50 k-6)/(2^k (3 k k))\' width=\'111\' height=\'67\' /> </subpod> <states count=\'1\'> <state name=\'More\' /> </states> <infos count=\'2\'> <info text=\'(n m) is the binomial coefficient\'> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP36319871d93ea43g0ga000064ehebh53g63hh35?MSPStoreType=image/gif&amp;s=57\' alt=\'(n m) is the binomial coefficient\' title=\'(n m) is the binomial coefficient\' width=\'195\' height=\'36\' /> <link url=\'http://reference.wolfram.com/mathematica/ref/Binomial.html\' text=\'Documentation\' title=\'Mathematica\' /> <link url=\'http://functions.wolfram.com/GammaBetaErf/Binomial\' text=\'Properties\' title=\'Wolfram Functions Site\' /> <link url=\'http://mathworld.wolfram.com/BinomialCoefficient.html\' text=\'Definition\' title=\'MathWorld\' /> </info> <info> <link url=\'http://functions.wolfram.com/Constants/Pi/06/ShowAll.html\' text=\'More information\' /> </info> </infos> </pod> <pod title=\'Integral representations\' scanner=\'MathematicalFunctionData\' id=\'{{&quot;IntegralRepresentations&quot;, &quot;MathematicalFunctionIdentityData&quot;}, {&quot;MathematicalFunctionDataScanner&quot;}}\' position=\'700\' error=\'false\' numsubpods=\'3\'> <subpod title=\'\'> <plaintext>pi = 2 integral_0^infinity1/(t^2+1) dt</plaintext> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP36419871d93ea43g0ga00001516a5235ae2dbe2?MSPStoreType=image/gif&amp;s=57\' alt=\'pi = 2 integral_0^infinity1/(t^2+1) dt\' title=\'pi = 2 integral_0^infinity1/(t^2+1) dt\' width=\'126\' height=\'45\' /> </subpod> <subpod title=\'\'> <plaintext>pi = 4 integral_0^1sqrt(1-t^2) dt</plaintext> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP36519871d93ea43g0ga0000617ca7idh6dgeec4?MSPStoreType=image/gif&amp;s=57\' alt=\'pi = 4 integral_0^1sqrt(1-t^2) dt\' title=\'pi = 4 integral_0^1sqrt(1-t^2) dt\' width=\'138\' height=\'45\' /> </subpod> <subpod title=\'\'> <plaintext>pi = 2 integral_0^infinity(sin(t))/t dt</plaintext> <img src=\'http://www1.wolframalpha.com/Calculate/MSP/MSP36619871d93ea43g0ga00002816ghg8475cgcee?MSPStoreType=image/gif&amp;s=57\' alt=\'pi = 2 integral_0^infinity(sin(t))/t dt\' title=\'pi = 2 integral_0^infinity(sin(t))/t dt\' width=\'124\' height=\'46\' /> </subpod> <states count=\'1\'> <state name=\'More\' /> </states> <infos count=\'1\'> <info> <link url=\'http://functions.wolfram.com/Constants/Pi/07/ShowAll.html\' text=\'More information\' /> </info> </infos> </pod> <assumptions count=\'1\'> <assumption type=\'Clash\' word=\'pi\' count=\'4\'> <value name=\'NamedConstant\' desc=\'a mathematical constant\' input=\'*C.pi-_*NamedConstant-\' /> <value name=\'Character\' desc=\'a character\' input=\'*C.pi-_*Character-\' /> <value name=\'Movie\' desc=\'a movie\' input=\'*C.pi-_*Movie-\' /> <value name=\'Word\' desc=\'a word\' input=\'*C.pi-_*Word-\' /> </assumption> </assumptions> </queryresult>', 'error' => 0, 'datatypes' => 'MathematicalFunctionIdentity', 'assumptions' => bless( { 'count' => '1', 'assumption' => [ bless( { 'count' => '4', 'word' => 'pi', 'value' => [ bless( { 'input' => '*C.pi-_*NamedConstant-', 'desc' => 'a mathematical constant', 'name' => 'NamedConstant' }, 'Net::WolframAlpha::AssumptionValue' ), bless( { 'input' => '*C.pi-_*Character-', 'desc' => 'a character', 'name' => 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