Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a850)

HypergeometricPFQ

$Mathematica Notation$

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=-5/2, a₃>=-5/2

For fixed z and a₁=-5/2, a₂=-5/2, a₃=3/2

For fixed z and a₁=-5/2, a₂=-5/2, a₃=3/2, b₁=4

http://functions.wolfram.com/07.27.03.a850.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 3/2}, {4, 4}, z] == (1/(2773437975 Pi^2 z^3)) (2048 (601490 + 9717250 z + 15381840 z^2 + 38339377 z^3 + 13299854 z^4 + 727332 z^5) EllipticE[1/2 - Sqrt[1 - z]/2]^ 2) - (1/(2773437975 Pi^2 z^3)) (2048 Sqrt[1 - z] (462890 + 6653835 z + 8335530 z^2 + 14622007 z^3 + 4093977 z^4 + 166320 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) - (1/(2773437975 Pi^2 z^3)) (2048 (601490 + 9717250 z + 15381840 z^2 + 38339377 z^3 + 13299854 z^4 + 727332 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(2773437975 Pi^2 z^3)) (1024 Sqrt[1 - z] (462890 + 6653835 z + 8335530 z^2 + 14622007 z^3 + 4093977 z^4 + 166320 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(2773437975 Pi^2 z^3)) (1024 (462890 + 6457040 z + 5765415 z^2 + 22957537 z^3 + 7684456 z^4 + 405246 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^ 2)

Standard Form

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MathML Form

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type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2773437975 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1024 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 405246 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7684456 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 22957537 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5765415 </cn> <apply> <power /> <ci> z </ci> <cn 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Rule Form

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

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]