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

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=-3/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(3/2), 6}, z] == (1/(178605 z^3)) (32 E^(z/2) (3243240 - 1590435 z + 493290 z^2 - 108360 z^3 + 117936 z^5 + 479136 z^6 + 396096 z^7 + 117504 z^8 + 13568 z^9 + 512 z^10) BesselI[0, z/2]) + (1/(178605 z^4)) (32 E^(z/2) (-12972960 + 6361740 z - 2378565 z^2 + 654570 z^3 - 143640 z^4 + 32256 z^5 - 26544 z^6 + 222624 z^7 + 297408 z^8 + 104704 z^9 + 13056 z^10 + 512 z^11) 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]