Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2770)

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=11/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=11/2, b₁=4

http://functions.wolfram.com/07.25.03.2770.01

Input Form

HypergeometricPFQ[{-(11/2), 11/2}, {4, 9/2}, z] == (1/(103378275 z)) (4 E^(z/2) (31185 + 26049870 z - 55301400 z^2 + 38953440 z^3 - 11884080 z^4 + 1695264 z^5 - 109632 z^6 + 2560 z^7) BesselI[0, z/2]) - (1/(103378275 z^2)) (4 E^(z/2) (124740 + 821205 z + 4220370 z^2 - 29882520 z^3 + 29303520 z^4 - 10345584 z^5 + 1589472 z^6 - 107072 z^7 + 2560 z^8) BesselI[1, z/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,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]