Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a8ba)

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=5, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=5, b₁=2

http://functions.wolfram.com/07.25.03.a8ba.01

Input Form

HypergeometricPFQ[{-(5/2), 5}, {2, 11/2}, -z] == (9 (2625 + 2800 z + 2660 z^2 + 8320 z^3 + 140144 z^4 + 81664 z^5 + 9152 z^6))/(E^z (2097152 z^4)) + (1/(4194304 z^(9/2))) (9 Sqrt[Pi] (-2625 - 1050 z - 1260 z^2 - 7000 z^3 + 98000 z^4 + 352800 z^5 + 172480 z^6 + 18304 z^7) 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]