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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.cdia.01

 Input Form

 Hypergeometric2F1[5, 6, -(35/8), z] == (1/1809658700365824) ((1/(-1 + z)^15) (16 (-113103668772864 + 2472123046035456 z - 28335161972097024 z^2 + 243211911934509056 z^3 - 2079427546142736384 z^4 + 38857416068692967424 z^5 + 214983048803136401249 z^6 + 246199125658778922504 z^7 + 79318851401173002624 z^8 + 5951747278048984064 z^9 + 18701318249349120 z^10)) - (1/(1 - z)^(123/8)) (473696720793450 (-1)^(1/8) (-1 + (-1)^(3/4)) z^(43/8) (1008015 + 3162400 z + 2572800 z^2 + 614400 z^3 + 32768 z^4) ArcTan[1 - (z^(1/8) Cos[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Sin[Pi/8])/(1 - z)^(1/8))]) - (1/(1 - z)^(123/8)) (473696720793450 (-1)^(1/8) (-1 + (-1)^(3/4)) z^(43/8) (1008015 + 3162400 z + 2572800 z^2 + 614400 z^3 + 32768 z^4) ArcTan[1 + (z^(1/8) Cos[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Sin[Pi/8])/(1 - z)^(1/8))]) + (1/(1 - z)^(123/8)) (473696720793450 (-1)^(3/8) (-1 + (-1)^(1/4)) z^(43/8) (1008015 + 3162400 z + 2572800 z^2 + 614400 z^3 + 32768 z^4) ArcTan[1 - (z^(1/8) Sin[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Cos[Pi/8])/(1 - z)^(1/8))]) + (1/(1 - z)^(123/8)) (473696720793450 (-1)^(3/8) (-1 + (-1)^(1/4)) z^(43/8) (1008015 + 3162400 z + 2572800 z^2 + 614400 z^3 + 32768 z^4) ArcTan[1 + (z^(1/8) Sin[Pi/8])/(1 - z)^(1/8), -((z^(1/8) Cos[Pi/8])/(1 - z)^(1/8))]) + (1/(1 - z)^(123/8)) (236848360396725 (-1)^(3/8) (-1 + (-1)^(1/4)) z^(43/8) (1008015 + 3162400 z + 2572800 z^2 + 614400 z^3 + 32768 z^4) Log[1 + z^(1/4)/(1 - z)^(1/4) - (2 z^(1/8) Cos[Pi/8])/(1 - z)^(1/8)]) - (1/(1 - z)^(123/8)) (236848360396725 (-1)^(3/8) (-1 + (-1)^(1/4)) z^(43/8) (1008015 + 3162400 z + 2572800 z^2 + 614400 z^3 + 32768 z^4) Log[1 + z^(1/4)/(1 - z)^(1/4) + (2 z^(1/8) Cos[Pi/8])/(1 - z)^(1/8)]) - (1/(1 - z)^(123/8)) (236848360396725 (-1)^(1/8) (-1 + (-1)^(3/4)) z^(43/8) (1008015 + 3162400 z + 2572800 z^2 + 614400 z^3 + 32768 z^4) Log[1 + z^(1/4)/(1 - z)^(1/4) - (2 z^(1/8) Sin[Pi/8])/(1 - z)^(1/8)]) + (1/(1 - z)^(123/8)) (236848360396725 (-1)^(1/8) (-1 + (-1)^(3/4)) z^(43/8) (1008015 + 3162400 z + 2572800 z^2 + 614400 z^3 + 32768 z^4) Log[1 + z^(1/4)/(1 - z)^(1/4) + (2 z^(1/8) Sin[Pi/8])/(1 - z)^(1/8)]))

 Standard Form

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 MathML Form

 2 F 1 ( 5 , 6 ; - 35 8 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["35", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] 1 1809658700365824 ( - 1 ( 1 - z ) 123 / 8 ( 473696720793450 - 1 8 ( - 1 + ( - 1 ) 3 / 4 ) ( 32768 z 4 + 614400 z 3 + 2572800 z 2 + 3162400 z + 1008015 ) tan - 1 ( 1 - z 8 cos ( π 8 ) 1 - z 8 , - z 8 sin ( π 8 ) 1 - z 8 ) z 43 / 8 ) - 1 ( 1 - z ) 123 / 8 ( 473696720793450 - 1 8 ( - 1 + ( - 1 ) 3 / 4 ) ( 32768 z 4 + 614400 z 3 + 2572800 z 2 + 3162400 z + 1008015 ) tan - 1 ( cos ( π 8 ) z 8 1 - z 8 + 1 , - z 8 sin ( π 8 ) 1 - z 8 ) z 43 / 8 ) + 1 ( 1 - z ) 123 / 8 ( 473696720793450 ( - 1 ) 3 / 8 ( - 1 + - 1 4 ) ( 32768 z 4 + 614400 z 3 + 2572800 z 2 + 3162400 z + 1008015 ) tan - 1 ( 1 - z 8 sin ( π 8 ) 1 - z 8 , - z 8 cos ( π 8 ) 1 - z 8 ) z 43 / 8 ) + 1 ( 1 - z ) 123 / 8 ( 473696720793450 ( - 1 ) 3 / 8 ( - 1 + - 1 4 ) ( 32768 z 4 + 614400 z 3 + 2572800 z 2 + 3162400 z + 1008015 ) tan - 1 ( sin ( π 8 ) z 8 1 - z 8 + 1 , - z 8 cos ( π 8 ) 1 - z 8 ) z 43 / 8 ) + 1 ( 1 - z ) 123 / 8 ( 236848360396725 ( - 1 ) 3 / 8 ( - 1 + - 1 4 ) ( 32768 z 4 + 614400 z 3 + 2572800 z 2 + 3162400 z + 1008015 ) log ( z 4 1 - z 4 - 2 cos ( π 8 ) z 8 1 - z 8 + 1 ) z 43 / 8 ) - 1 ( 1 - z ) 123 / 8 ( 236848360396725 ( - 1 ) 3 / 8 ( - 1 + - 1 4 ) ( 32768 z 4 + 614400 z 3 + 2572800 z 2 + 3162400 z + 1008015 ) log ( z 4 1 - z 4 + 2 cos ( π 8 ) z 8 1 - z 8 + 1 ) z 43 / 8 ) - 1 ( 1 - z ) 123 / 8 ( 236848360396725 - 1 8 ( - 1 + ( - 1 ) 3 / 4 ) ( 32768 z 4 + 614400 z 3 + 2572800 z 2 + 3162400 z + 1008015 ) log ( z 4 1 - z 4 - 2 sin ( π 8 ) z 8 1 - z 8 + 1 ) z 43 / 8 ) + 1 ( 1 - z ) 123 / 8 ( 236848360396725 - 1 8 ( - 1 + ( - 1 ) 3 / 4 ) ( 32768 z 4 + 614400 z 3 + 2572800 z 2 + 3162400 z + 1008015 ) log ( z 4 1 - z 4 + 2 sin ( π 8 ) z 8 1 - z 8 + 1 ) z 43 / 8 ) + 1 ( z - 1 ) 15 ( 16 ( 18701318249349120 z 10 + 5951747278048984064 z 9 + 79318851401173002624 z 8 + 246199125658778922504 z 7 + 214983048803136401249 z 6 + 38857416068692967424 z 5 - 2079427546142736384 z 4 + 243211911934509056 z 3 - 28335161972097024 z 2 + 2472123046035456 z - 113103668772864 ) ) ) HypergeometricPFQ 5 6 -1 35 8 z 1 1809658700365824 -1 1 1 -1 z 123 8 -1 473696720793450 -1 1 8 -1 -1 3 4 32768 z 4 614400 z 3 2572800 z 2 3162400 z 1008015 1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 z 43 8 -1 1 1 -1 z 123 8 -1 473696720793450 -1 1 8 -1 -1 3 4 32768 z 4 614400 z 3 2572800 z 2 3162400 z 1008015 8 -1 z 1 8 1 -1 z 1 8 -1 1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 z 43 8 1 1 -1 z 123 8 -1 473696720793450 -1 3 8 -1 -1 1 4 32768 z 4 614400 z 3 2572800 z 2 3162400 z 1008015 1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 z 43 8 1 1 -1 z 123 8 -1 473696720793450 -1 3 8 -1 -1 1 4 32768 z 4 614400 z 3 2572800 z 2 3162400 z 1008015 8 -1 z 1 8 1 -1 z 1 8 -1 1 -1 z 1 8 8 -1 1 -1 z 1 8 -1 z 43 8 1 1 -1 z 123 8 -1 236848360396725 -1 3 8 -1 -1 1 4 32768 z 4 614400 z 3 2572800 z 2 3162400 z 1008015 z 1 4 1 -1 z 1 4 -1 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 z 43 8 -1 1 1 -1 z 123 8 -1 236848360396725 -1 3 8 -1 -1 1 4 32768 z 4 614400 z 3 2572800 z 2 3162400 z 1008015 z 1 4 1 -1 z 1 4 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 z 43 8 -1 1 1 -1 z 123 8 -1 236848360396725 -1 1 8 -1 -1 3 4 32768 z 4 614400 z 3 2572800 z 2 3162400 z 1008015 z 1 4 1 -1 z 1 4 -1 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 z 43 8 1 1 -1 z 123 8 -1 236848360396725 -1 1 8 -1 -1 3 4 32768 z 4 614400 z 3 2572800 z 2 3162400 z 1008015 z 1 4 1 -1 z 1 4 -1 2 8 -1 z 1 8 1 -1 z 1 8 -1 1 z 43 8 1 z -1 15 -1 16 18701318249349120 z 10 5951747278048984064 z 9 79318851401173002624 z 8 246199125658778922504 z 7 214983048803136401249 z 6 38857416068692967424 z 5 -1 2079427546142736384 z 4 243211911934509056 z 3 -1 28335161972097024 z 2 2472123046035456 z -113103668772864 [/itex]

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2007-05-02