Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aeap)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=6, b₁>=-11/2

For fixed z and a₁=1/2, a₂=6, b₁=-11/2

http://functions.wolfram.com/07.25.03.aeap.01

Input Form

HypergeometricPFQ[{1/2, 6}, {-(11/2), -(5/2)}, z] == (1/2338875) (2338875 + 510300 z + 396900 z^2 + 1512000 z^3 - 9525600 z^4 + 38102400 z^5 - 307359360 z^6 - 833798880 z^7 - 631819800 z^8 - 215003880 z^9 - 38289420 z^10 - 3777504 z^11 - 205952 z^12 - 5760 z^13 - 64 z^14) - (1/2338875) (2 E^z Sqrt[Pi] (280816200 z^(13/2) + 538231050 z^(15/2) + 362032650 z^(17/2) + 116246025 z^(19/2) + 20041050 z^(21/2) + 1938840 z^(23/2) + 104400 z^(25/2) + 2896 z^(27/2) + 32 z^(29/2)) Erf[Sqrt[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,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},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]