Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1767)

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=-11/2, a₂>=-11/2

For fixed z and a₁=-11/2, a₂=3, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=3, b₁=7/2

http://functions.wolfram.com/07.25.03.1767.01

Input Form

HypergeometricPFQ[{-(11/2), 3}, {7/2, 4}, z] == 6/(221 z^3) + (1/(1520762880 z^3)) (E^z (-41287680 - 62090595 z - 135508590 z^2 + 850707900 z^3 - 635946120 z^4 + 176702064 z^5 - 22015904 z^6 + 1232192 z^7 - 24960 z^8)) + (1/(3041525760 z^(5/2))) (Sqrt[Pi] (103378275 + 183783600 z + 771891120 z^2 - 2205403200 z^3 + 1429428000 z^4 - 374250240 z^5 + 45239040 z^6 - 2489344 z^7 + 49920 z^8) Erfi[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]