Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aj1s)

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=7/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.aj1s.01

Input Form

HypergeometricPFQ[{5/2, 7/2}, {-(5/2), 2}, z] == (1/675) E^(z/2) (675 - 1440 z + 2520 z^2 - 9360 z^3 - 26640 z^4 - 14400 z^5 - 2496 z^6 - 128 z^7) BesselI[0, z/2] + (1/675) E^(z/2) (-315 + 720 z - 1080 z^2 + 2160 z^3 - 15600 z^4 - 12096 z^5 - 2368 z^6 - 128 z^7) 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]