Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7vd)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a7vd.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, 23/4}, -z] == (Sqrt[Pi] (-43673516350088625 - 419265756960850800 z + 813121468045286400 z^2 - 619521118510694400 z^3 + 450560813462323200 z^4 + 480598201026478080 z^5 + 53961903273148416 z^6 + 1787557872402432 z^7 + 20371029884928 z^8 + 68719476736 z^9) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-14557838783362875 + 48538704793924800 z - 37497685004881920 z^2 + 23664505632768000 z^3 + 29447746827190272 z^4 + 3352182317383680 z^5 + 111485405626368 z^6 + 1272384061440 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (43673516350088625 + 9402782656176000 z - 21435158330127360 z^2 + 9376906058956800 z^3 + 27248223279513600 z^4 + 3272437395357696 z^5 + 110544606461952 z^6 + 1269162835968 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/(571500855350525952 z^(19/4))

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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]