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

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=9/2, a₂=11/2, b₁=-7/2

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

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(7/2), 3}, z] == (1/10418625) (16 E^(z/2) (680400 - 1828575 z + 3364200 z^2 - 7040250 z^3 + 34050240 z^4 + 131261760 z^5 + 115637760 z^6 + 42560640 z^7 + 7649280 z^8 + 698112 z^9 + 30720 z^10 + 512 z^11) BesselI[0, z/2]) + (1/(10418625 z)) (4 E^(z/2) (-467775 - 510300 z + 2986200 z^2 - 5859000 z^3 + 10591560 z^4 - 26933760 z^5 + 244984320 z^6 + 330739200 z^7 + 143481600 z^8 + 27982848 z^9 + 2672640 z^10 + 120832 z^11 + 2048 z^12) 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]