Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1903)

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=-7/2, a₃>=-7/2

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

For fixed z and a₁=-7/2, a₂=-7/2, a₃=5/2, b₁=3

http://functions.wolfram.com/07.27.03.1903.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 5/2}, {3, 4}, z] == (1/(200876150475 Pi^2 z^3)) (1024 (-970200 - 56615440 z + 512033585 z^2 + 8665123634 z^3 + 13587880018 z^4 + 4576104184 z^5 + 251840800 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2) - (1/(200876150475 Pi^2 z^3)) (1024 Sqrt[1 - z] (-970200 - 36362515 z + 352956100 z^2 + 3975076104 z^3 + 5133676699 z^4 + 1408750040 z^5 + 57657600 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) - (1/(200876150475 Pi^2 z^3)) (1024 (-970200 - 56615440 z + 512033585 z^2 + 8665123634 z^3 + 13587880018 z^4 + 4576104184 z^5 + 251840800 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(200876150475 Pi^2 z^3)) (512 Sqrt[1 - z] (-970200 - 36362515 z + 352956100 z^2 + 3975076104 z^3 + 5133676699 z^4 + 1408750040 z^5 + 57657600 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(200876150475 Pi^2 z^3)) (512 (-970200 - 35877415 z + 366104445 z^2 + 5408070814 z^3 + 8122894732 z^4 + 2644055577 z^5 + 140334800 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2)

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]