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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] > Specific values > For integer and half-integer parameters and fixed z > For fixed z and a1=-7/2, a2>=-7/2 > For fixed z and a1=-7/2, a2=3, a3>=3 > For fixed z and a1=-7/2, a2=3, a3=3 > For fixed z and a1=-7/2, a2=3, a3=3, b1=-5/2





http://functions.wolfram.com/07.27.03.9209.01









  


  










Input Form





HypergeometricPFQ[{-(7/2), 3, 3}, {-(5/2), -(1/2)}, -z] == (1/(10240 (1 + z)^5)) (10240 + 309248 z - 4459640 z^2 + 71268180 z^3 + 36018675 Pi^2 z^(7/2) + 513347340 z^4 + 180093375 Pi^2 z^(9/2) + 1188011880 z^5 + 360186750 Pi^2 z^(11/2) + 1296031968 z^6 + 360186750 Pi^2 z^(13/2) + 688356900 z^7 + 180093375 Pi^2 z^(15/2) + 144074700 z^8 + 36018675 Pi^2 z^(17/2)) + (1/(15728640 (1 + z)^(25/2))) ((-15728640 - 780215808 z + 8992646400 z^2 - 185389467200 z^3 - 3904864012000 z^4 - 36932368006520 z^5 - 154036066578436 z^6 - 446091226753400 z^7 - 893869247117575 z^8 - 1304291646409175 z^9 - 1408872325482055 z^10 - 1130347322026433 z^11 - 666718543842750 z^12 - 281440941516000 z^13 - 80604526564800 z^14 - 14049733824000 z^15 - 1126356295680 z^16) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(15728640 (1 + z)^(25/2))) ((15728640 + 780215808 z - 8992646400 z^2 + 185389467200 z^3 + 3904864012000 z^4 + 36932368006520 z^5 + 154036066578436 z^6 + 446091226753400 z^7 + 893869247117575 z^8 + 1304291646409175 z^9 + 1408872325482055 z^10 + 1130347322026433 z^11 + 666718543842750 z^12 + 281440941516000 z^13 + 80604526564800 z^14 + 14049733824000 z^15 + 1126356295680 z^16) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (1/(512 (1 + z)^(11/2))) (21 (-2450 z^(3/2) + 26215 z^(5/2) + 644292 z^(7/2) + 2514501 z^(9/2) + 4371246 z^(11/2) + 3956337 z^(13/2) + 1829520 z^(15/2) + 343035 z^(17/2)) Log[Sqrt[z] + Sqrt[1 + z]]) + (1/(15728640 (1 + z)^(25/2))) ((15728640 + 780215808 z - 8992646400 z^2 + 185389467200 z^3 + 3904864012000 z^4 + 36932368006520 z^5 + 154036066578436 z^6 + 446091226753400 z^7 + 893869247117575 z^8 + 1304291646409175 z^9 + 1408872325482055 z^10 + 1130347322026433 z^11 + 666718543842750 z^12 + 281440941516000 z^13 + 80604526564800 z^14 + 14049733824000 z^15 + 1126356295680 z^16) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (7203735/512) z^(7/2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])] + (7203735/512) z^(7/2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))] - (7203735/512) z^(7/2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])]










Standard Form





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MathML Form







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&#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 1126356295680 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 16 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 14049733824000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 15 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 80604526564800 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 14 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 281440941516000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 13 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 666718543842750 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 12 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1130347322026433 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1408872325482055 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1304291646409175 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 893869247117575 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 446091226753400 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 154036066578436 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 36932368006520 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3904864012000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 185389467200 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8992646400 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 780215808 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 15728640 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> - </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 15728640 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 25 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1126356295680 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 16 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 14049733824000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 15 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 80604526564800 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 14 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 281440941516000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 13 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 666718543842750 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 12 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1130347322026433 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 11 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1408872325482055 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1304291646409175 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 893869247117575 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 446091226753400 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 154036066578436 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 36932368006520 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3904864012000 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 185389467200 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8992646400 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 780215808 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 15728640 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 512 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 21 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 343035 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 17 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1829520 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 15 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3956337 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4371246 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2514501 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 644292 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 26215 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2450 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 15728640 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 25 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1126356295680 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 16 </mn> 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</mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <cn type='integer'> 3 </cn> <cn type='integer'> 3 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 7203735 <sep /> 512 </cn> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> 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Date Added to functions.wolfram.com (modification date)





2007-05-02