Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.3009)

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=-5/2, a₃>=-5/2

For fixed z and a₁=-7/2, a₂=-5/2, a₃=2

For fixed z and a₁=-7/2, a₂=-5/2, a₃=2, b₁=4

http://functions.wolfram.com/07.27.03.3009.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 2}, {4, 4}, z] == (64 (8 + 143 z))/(99099 z^3) + (1/(4463914455 Pi z^3)) (256 (-645647 - 7090870 z + 8964415 z^2 + 67428172 z^3 + 48131231 z^4 + 6389194 z^5 + 31185 z^6) EllipticE[z]) + (1/(4463914455 Pi z^3)) (256 (465467 + 3592374 z - 11730947 z^2 - 28275628 z^3 + 15477381 z^4 + 18437398 z^5 + 2033955 z^6) EllipticK[z])

Standard Form

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MathML Form

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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]